The books are structured as a series of dreams in which Mr Tompkins enters alternate worlds where the physical constants have radically different values from those they have in the real world. This results in the counterintuitive results of the theory of relativity and quantum mechanics becoming obvious in everyday life.
Mr Tompkins' adventures begin when he chooses to spend the afternoon of a day's holiday attending a lecture on the theory of relativity. The lecture proves less comprehensible than he had hoped and he drifts off to sleep and enters a dream world in which the speed of light is a mere 10 miles an hour. This becomes apparent to him through the fact that passing cyclists are subject to a noticeable Lorentz–FitzGerald contraction.
Despite this inauspicious beginning to his scientific education, Mr Tompkins becomes acquainted with the Professor delivering the lectures and ultimately marries the Professor's daughter, Maud. Later chapters in the books deal with atomic structure (Mr Tompkins spends time as a conduction electron, returning to consciousness when he is annihilated in an encounter with a positron) and thermodynamics (the Professor expounds an analogy between the second law of thermodynamics and the bias towards the casino in gambling before being confounded by a local reversal of the second law through the intervention of Maxwell's demon who has introduced himself to Maud in one of her dreams).
Later books in the series tackled biology (a subject taken up by the son of Mr and Mrs Tompkins who has inherited the Professor's academic leanings) and advanced cosmology.
In 2010 the first volume of a proposed ten-issue comic book series, The Adventures of Mr. Tompkins, was created by Igor Gamow, George Gamow's son, and illustrator Scorpio Steele. In the book Tompkins learns about relativity from Albert Einstein, radioactivity from Marie Curie and the structure of the atom from Ernest Rutherford. A second volume, in which Tompkins meets Charles Darwin, Gregor Mendel and James D. Watson, was published in July 2011.
- George Gamow, Mr Tompkins in Wonderland, first published in 1940
- George Gamow, Mr Tompkins explores the atom, first published in 1944
- George Gamow, Mr Tompkins learns the facts of life, Cambridge University Press, 1953
- George Gamow and Martynas Ycas Mr Tompkins inside himself: Adventures in the new biology, Viking Press, 1967
- George Gamow, Roger Penrose (Foreword), Mr. Tompkins in Paperback (Omnibus of Mr. Tompkins in Wonderland and Mr Tompkins Explores the Atom), Cambridge University Press, 1993, ISBN 0-521-44771-2
- George Gamow, Russell Stannard (Editor), Michael Edwards (Illustrator), The New World of Mr Tompkins, Cambridge University Press, 2001 (revised and updated edition), ISBN 0-521-63992-1
- Igor Gamow (Writer), Scorpio Steele (Illustrator), The Adventures of Mr. Tompkins, CreateSpace, 2010 ISBN 1-4392-5211-4
- Igor Gamow (Writer), Scorpio Steele (Illustrator), The Adventures of Mr. Tompkins, No. 2, CreateSpace, 2011 ISBN 1-4611-9559-4