By Jan Hendrik Bruinier, Gerard van der Geer, Günter Harder, Don Zagier, Kristian Ranestad

From the reviews:

"Zagier … offers 28 wonderful functions, beginning with type numbers, ranging via drums of ‘unhearable’ form, percolation, nonlinear differential equations, and finishing with primes that equivalent the sum of 2 cubes. … Summing Up: hugely instructed. Upper-division undergraduate via expert collections." (D. V. Feldman, selection, Vol. forty six (7), March, 2009)

"The authors of The 1-2-3 of Modular varieties reach offering a … thorough account of the idea of modular varieties in a number of guises and purposes, discussing in additional element the themes pointed out right here in addition to many extra. certainly, as a result of either its breadth and clarity, this ebook may be an invaluable resource for mathematicians, either amateur and professional, wishing to learn extra approximately modular kinds and a gorgeous theory." (Amanda Folsom, Bulletin of the yank Mathematical Society, Vol. forty six (3), July, 2009)

“If you ever desired to achieve a normal figuring out of modular kinds … you then should still try out The 1-2-3 of Modular varieties. … each one set of lectures contains commonplace introductory fabric in addition to concrete examples and purposes. … you can actually use this with a view to begin a graduate pupil engaged on modular types … . even if you're looking for a pleasant technique to start your research … or are already accustomed to them, it is a publication that you'll enjoy.” (Suzanne Caulk, The Mathematical organization of the USA, September, 2010)