Escher is not the first Artist to explore mathematical themes: Parmigianino (1503–1540) had explored spherical geometry and reflection in his 1524 Self-portrait in a Convex Mirror, depicting his own image in a curved mirror, while william Hogarth's 1754 Satire on False Perspective foreshadows Escher's playful exploration of errors in perspective. Another early artistic forerunner is Giovanni Battista Piranesi (1720–1778), whose dark "fantastical" prints such as The Drawbridge in his Carceri ("Prisons") sequence depict perspectives of complex architecture with many stairs and ramps, peopled by walking figures. Only with 20th century movements such as Cubism, De Stijl, Dadaism, and Surrealism did mainstream art start to explore Escher-like ways of looking at the world with multiple simultaneous viewpoints. However, although Escher had much in Common with, for Example, Magritte's surrealism, he did not make contact with any of these movements.

Maurits Cornelis Escher was born on 17 June 1898 in Leeuwarden, Friesland, the Netherlands, in a house that forms part of the Princessehof Ceramics Museum today. He was the youngest son of the civil Engineer George Arnold Escher and his second wife, Sara Gleichman. In 1903, the family moved to Arnhem, where he attended primary and secondary school until 1918. Known to his friends and family as "Mauk", he was a sickly child and was placed in a special school at the age of seven; he failed the second grade. Although he excelled at drawing, his grades were generally poor. He took carpentry and piano lessons until he was thirteen years old.

In 1918, he went to the Technical College of Delft. From 1919 to 1922, Escher attended the Haarlem School of Architecture and Decorative Arts, learning drawing and the art of making woodcuts. He briefly studied architecture, but he failed a number of subjects (due partly to a persistent skin infection) and switched to decorative arts, studying under the graphic Artist Samuel Jessurun de Mesquita.

In 1922, an important year of his life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello. In the same year, he traveled through Spain, visiting Madrid, Toledo, and Granada. He was impressed by the Italian countryside and, in Granada, by the Moorish architecture of the fourteenth-century Alhambra. The intricate decorative designs of the Alhambra, based on geometrical symmetries featuring interlocking repetitive patterns in the coloured tiles or sculpted into the walls and ceilings, triggered his interest in the mathematics of tessellation and became a powerful influence on his work.

Escher returned to Italy and lived in Rome from 1923 to 1935. While in Italy, Escher met Jetta Umiker – a Swiss woman, like himself attracted to Italy – whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grandfather, was born. Escher and Jetta later had two more sons — Arthur and Jan.

He travelled frequently, visiting (among other places) Viterbo in 1926, the Abruzzi in 1927 and 1929, Corsica in 1928 and 1933, Calabria in 1930, the Amalfi coast in 1931 and 1934, and Gargano and Sicily in 1932 and 1935. The townscapes and landscapes of these places feature prominently in his artworks. In May and June 1936, Escher travelled back to Spain, revisiting the Alhambra and spending days at a time making detailed drawings of its mosaic patterns. It was here that he became fascinated, to the point of obsession, with tessellation, explaining:

The Netherlands post office had Escher design a semi-postal stamp for the "Air Fund" in 1935, and again in 1949 he designed Netherlands stamps. These were for the 75th anniversary of the Universal Postal Union; a different design was used by Surinam and the Netherlands Antilles for the same commemoration.

The mathematical influence in his work became prominent after 1936, when, having boldly asked the Adria Shipping Company if he could sail with them as travelling Artist in return for making drawings of their ships, they surprisingly agreed, and he sailed the Mediterranean, becoming interested in order and symmetry. Escher described this journey, including his repeat visit to the Alhambra, as "the richest source of inspiration I have ever tapped".

His first study of mathematics began with papers by George Pólya and by the crystallographer Friedrich Haag on plane symmetry groups, sent to him by his brother Berend, a Geologist. He carefully studied the 17 canonical wallpaper groups and created periodic tilings with 43 drawings of different types of symmetry. From this point on, he developed a mathematical approach to expressions of symmetry in his artworks using his own notation. Starting in 1937, he created woodcuts based on the 17 groups. His Metamorphosis I (1937) began a series of designs that told a story through the use of pictures. In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. He extended the approach in his piece Metamorphosis III, which is four metres long.

In 1941 and 1942, Escher summarized his findings for his own artistic use in a sketchbook, which he labeled (following Haag) Regelmatige vlakverdeling in asymmetrische congruente veelhoeken ("Regular division of the plane with asymmetric congruent polygons"). The Mathematician Doris Schattschneider unequivocally described this notebook as recording "a methodical investigation that can only be termed mathematical research." She defined the research questions he was following as

Escher's artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. His interest in the multiple levels of reality in art is seen in works such as Drawing Hands (1948), where two hands are shown, each drawing the other. The critic Steven Poole commented that

In 1954, the International Congress of Mathematicians met in Amsterdam, and N. G. de Bruin organized a display of Escher's work at the Stedelijk Museum for the participants. Both Roger Penrose and H. S. M. Coxeter were deeply impressed with Escher's intuitive grasp of mathematics. Inspired by Relativity, Penrose devised his tribar, and his father, Lionel Penrose, devised an endless staircase. Roger Penrose sent sketches of both objects to Escher, and the cycle of invention was closed when Escher then created the perpetual motion machine of Waterfall and the endless march of the monk-figures of Ascending and Descending. In 1957, Coxeter obtained Escher's permission to use two of his drawings in his paper "Crystal symmetry and its generalizations". He sent Escher a copy of the paper; Escher recorded that Coxeter's figure of a hyperbolic tessellation "gave me quite a shock": the infinite regular repetition of the tiles in the hyperbolic plane, growing rapidly smaller towards the edge of the circle, was precisely what he wanted to allow him to represent infinity on a two-dimensional plane.

In his early years, Escher sketched landscapes and nature. He also sketched insects such as ants, bees, grasshoppers, and mantises,, which appeared frequently in his later work. His early love of Roman and Italian landscapes and of nature created an interest in tessellation, which he called Regular Division of the Plane; this became the title of his 1958 book, complete with reproductions of a series of woodcuts based on tessellations of the plane, in which he described the systematic buildup of mathematical designs in his artworks. He wrote, "Mathematicians have opened the gate leading to an extensive domain".

Escher's interest in curvilinear perspective was encouraged by his friend and "kindred spirit", the art Historian and Artist Albert Flocon, in another Example of constructive mutual influence. Flocon identified Escher as a "thinking artist" alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon. Flocon was delighted by Escher's Grafiek en tekeningen ("Graphics in Drawing"), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher and to write the book La Perspective curviligne ("Curvilinear perspective").

Escher was also fascinated by mathematical objects such as the Möbius strip, which has only one surface. His wood engraving Möbius Strip II (1963) depicts a chain of ants marching forever over what, at any one place, are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface. In Escher's own words:

Escher's fame in popular culture grew when his work was featured by Martin Gardner in his April 1966 "Mathematical Games" column in Scientific American. Escher's works have appeared on many album covers including The Scaffold's 1969 L the P with Ascending and Descending; Mott the Hoople's eponymous 1969 record with Reptiles, Beaver & Krause's 1970 In A Wild Sanctuary with Three Worlds; and Mandrake Memorial's 1970 Puzzle with House of Stairs and (inside) Curl Up. His works have similarly been used on many book covers, including some editions of Edwin Abbott's Flatland, which used Three Spheres; E. H. Gombrich's Meditations on a Hobby Horse with Horseman; Pamela Hall's Heads You Lose with Plane Filling 1; Patrick A. Horton's Mastering the Power of Story with Drawing Hands; Erich Gamma et al.'s Design Patterns: Elements of Reusable Object-oriented software with Swans; and Arthur Markman's Knowledge Representation with Reptiles. The "World of Escher" markets posters, neckties, T-shirts, and jigsaw puzzles of Escher's artworks. Both Austria and the Netherlands have issued postage stamps commemorating the Artist and his works.

In July 1969 he finished his last work, a large woodcut with threefold rotational symmetry called Snakes, in which snakes wind through a pattern of linked rings. These shrink to infinity toward both the center and the edge of a circle. It was exceptionally elaborate, being printed using three blocks, each rotated three times about the center of the image and precisely aligned to avoid gaps and overlaps, for a total of nine print operations for each finished print. The image encapsulates Escher's love of symmetry; of interlocking patterns; and, at the end of his life, of his approach to infinity. The care that Escher took in creating and printing this woodcut can be seen in a video recording.

Escher moved to the Rosa Spier Huis in Laren in 1970, an artists' retirement home in which he had his own studio. He died in a hospital in Hilversum on 27 March 1972, aged 73. He is buried at the New Cemetery in Baarn.

The Pulitzer Prize-winning 1979 book Gödel, Escher, Bach by Douglas Hofstadter discusses the ideas of self-reference and strange loops, drawing on a wide range of artistic and scientific sources including Escher's art and the music of J. S. Bach.

Despite wide popular interest, Escher was for a long time somewhat neglected in the art world; even in his native Netherlands, he was 70 before a retrospective exhibition was held. In the twenty-first century, major exhibitions have been held in cities across the world. An exhibition of his work in Rio de Janeiro attracted more than 573,000 visitors in 2011; its daily visitor count of 9,677 made it the most visited museum exhibition of the year, anywhere in the world. No major exhibition of Escher's work was held in Britain until 2015, when the Scottish National Gallery of Modern Art ran one in Edinburgh from June to September 2015, moving in October 2015 to the Dulwich Picture Gallery, London. The exhibition moved to Italy in 2015–2016, attracting over 500,000 visitors in Rome and Bologna, and then Milan.

Escher carefully studied Coxeter's figure, marking it up to analyse the successively smaller circles with which (he deduced) it had been constructed. He then constructed a diagram, which he sent to Coxeter, showing his analysis; Coxeter confirmed it was correct, but disappointed Escher with his highly technical reply. All the same, Escher persisted with hyperbolic tiling, which he called "Coxetering". Among the results were the series of wood engravings Circle Limit I–IV. In 1959, Coxeter published his finding that these works were extraordinarily accurate: "Escher got it absolutely right to the millimeter".

Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—his art had a strong mathematical component, and several of the worlds that he drew were built around impossible objects. After 1924, Escher turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. His first print of an impossible reality was Still Life and Street (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as Relativity (1953). House of Stairs (1951) attracted the interest of the Mathematician Roger Penrose and his father, the Biologist Lionel Penrose. In 1956, they published a paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' continuously rising flights of steps, and enclosed a print of Ascending and Descending (1960). The paper also contained the tribar or Penrose triangle, which Escher used repeatedly in his lithograph of a building that appears to function as a perpetual motion machine, Waterfall (1961).