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Probability Theory Book

borovkov - probability theory
cinlar - probability and stochastic
grimmett - probability and random processes (is the standard book for probability for most graduate courses and has solutions)
klenke - probability theory
gut - probability a graduate course
koralov - theory of probability and random processes (concise and easy to read)
stroock - mathematics of probability (beautifully written)
stroock - probability theory an analytic view
shiryaev - probability theory
loeve - probability theory (multiple volumes)
feller - probability theory (multiple volumes, really good read)
wise - counterexamples in probability and real analysis
lahiri - measure theory and probability theory
jorgensen - probability theory with a view towards statistics
dudley - real analysis and probability
durrett - probability theory with examples
capinski - probability through problems (exercise book)
meyer - probability and potentials

an elementary book is the following

ross - an introduction to probability models (with solutions)
 
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