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In the last five years there has been very significant progress in
the development of transcendence theory. A new approach to the
arithmetic properties of values of modular forms and
theta-functions was found. The solution of the Mahler-Manin problem
on values of modular function j(tau) and algebraic independence of
numbers pi and e DEGREES(pi) are most impressive results of this
breakthrough. The book presents these and other results on
algebraic independence of numbers and further, a detailed
exposition of methods created in last the 25 years, during which
commutative algebra and algebraic geometry exerted strong catalytic
influence on the development of the s
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