Probability Theory / Springer Textbook (PDF)

Sinai's book leads the student through the standard material
for ProbabilityTheory, with stops along the way for
interesting topics such as statistical mechanics, not
usually included in a book for beginners.
The first part of the book covers discrete random variables,
using the same approach, basedon Kolmogorov's axioms for
probability, used later for the general case.
The text is divided into sixteen lectures, each covering a
major topic. The introductory notions and classical results
are included, of course: random variables, the central limit
theorem, the law of large numbers, conditional probability,
random walks, etc. Sinai's style is accessible and clear,
with interesting examples to accompany new ideas.
Besides statistical mechanics, other interesting, less
common topics found in the book are: percolation, the
concept of stability in the central limit theorem and the
study of probability of large deviations.
Little more than a standard undergraduate course in analysis
is assumed of the reader. Notions from measure theory and
Lebesgue integration are introduced in the second half of
the text.
The book is suitable for second or third year students in
mathematics, physics or other natural sciences. It could
also be usedby more advanced readers who want to learn the
mathematics of probability theory and some of its
applications in statistical physics.