It was in Arnhem that as a young boy, Mauk received lessons in carpentry from a contractor's apprentice, Van Eldik. During that time, he developed a love for working with wood and learned how to remove the grain patiently from the surface of a plank of pear wood, a technique that would later be of practical use in producing fine woodcuts. 

From 1912 to 1918, he attended the hogere burgerschool (H.B.S., public high school) in Arnhem. Although he was not particularly good in his lessons in mathematics and the sciences, he absorbed the attitude and methodological approach of the scientist at home. He once wrote in a letter, "My affinity with the exact approach to natural phenomena is probably related to the milieu in which I grew up as a boy: my father and three of my brothers were all trained in the exact sciences or engineering, and I have always had an enormous respect for these things" . His father, a civil engineer, was a keenly observant and methodical person, open and matter of fact, and he seems to have passed these qualities on to Mauk.

In high school, drawing was the one subject which he enjoyed. He preferred to draw in black and white and often made drawings at home. He showed these drawings to his art teacher, F. W. van der Haagen, who recognized and encouraged Escher's talent, and taught him how to make linoleum cuts. Escher's first prints were mostly portraits or bookplates; the earliest dated one, done in 1916, is of his father. He also made a few etchings; these he felt were unsuccessful. 

In the fall of 1917, then a senior at the H.B.S., Escher sent some of his linoleum prints to the well-known Dutch graphic artist R. N. Roland Holst and asked for his opinion. Holst sent a kind reply almost immediately and encouraged him to send further work. The following June, Escher sent him a couple more prints. In the fall of 1918, Escher attended lectures at the Higher Technical School in Delft in order to retake some of his final examinations which he had failed in August, but health problems finally led him to give up his studies, and he concentrated on his drawings. In February 1919 he visited Roland Holst, then a professor at the Rijks-Academy in Amsterdam, and talked about his future. Roland Holst strongly advised him to begin making woodcuts and to consider studying architecture at the university in Zurich. 

Escher immediately made a woodcut; a small piece of wood for a bookplate was all he could afford. The design was for his close friend Roosje and showed a single rose, together with her initials. He wrote enthusiastically about the graphic technique in his letter to her. "It is splendid work, but much more difficult than working in linoleum, because it is terribly hard to cut palm wood against the grain."

Escher was further encouraged when, a short while later, the first published review of his work-some linoleum prints he had entered in the annual exhibition of the Artibus Sacrurn society  appeared in the weekly paper De Hofstad (The Court Capital). "The works that first attract our attention include the beautiful woodcuts by M. C. Escher, who entered a few portraits and a sunflower, soberly executed and with a beautiful contrast between black and white." Escher added the question mark to his clipping of the review; the linocuts were mistaken for woodcuts.

The following September Escher moved to Haarlem to attend the School for Architecture and Decorative Arts with the intention of preparing for a career as an architect. Soon after he began his classes, he met Samuel Jessurun de Mesquita, who taught nature drawing and graphic arts. Escher showed deMesquita his graphic work, and the teacher advised him to devote his studies to the graphic arts.

With a growing interested in graphics, he spent a number of years travelling in Europe. He married Jetta Umiker in 1921 and lived in Rome. His works at this time depict landscapes using impossible perspectives.

Fascism in Italy in the1930s made life impossible for Escher and his family and they moved to Switzerland. In 1936 Escher made an important journey to the Alhambra in Granada, Spain. He was fascinated by Islamic art depicted in the Moorish tilings he saw there and some time after his visit he read Pólya's 1924 paper on plane symmetry groups. 

Although he did not understand the abstract concept of groups discussed in Pólya's paper he did understand the 17 plane symmetry groups described there. Between 1936 and 1941 Escher worked on possible periodic tilings producing 43 coloured drawings with a wide variety of symmetry types. He adopted a highly mathematical approach with a systematic study using notation which he invented himself. 

After spending a while in Belgium, Escher returned to the Netherlands in 
1941. His fame slowly spread and articles appeared on his work during the 1950s. His works began to be displayed in science museums rather than art galleries. 

Escher corresponded with several mathematicians for example Pólya and Coxeter. A number of quotes by Escher show his relation with mathematics and mathematicians. " I have often felt closer to people who work scientifically (though I certainly do not do so myself) than to my fellow artists." 

Again in Regular Division of the Plane Escher writes:-   In mathematical quarters, the regular division of the plane has been considered  theoretically [Mathematicians] have opened the gate leading to  an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it. 

In his last years are described as follows:- When Escher's view of the world turned inward he produced his best  known puzzling prints which, art aside, were truly intellectually playful, yet he was not. His life turned inward, he cut himself off and he had few friends. ... He died in 27 March 1972 in Laren, Netherlands after a protracted illness...