Sets, Relations, Functions  
This free book gives a gentle introduction to the set theoretic tools needed by anyone who comes into contact with modern Mathematics. The intended audience are students of any subject or practitioners who need some knowledge of set operations and related topics. 
Basic Concepts of Mathematics  
This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers and etc. 
Mathematical Analysis I  
This free text carefully leads the student through the basic topics of undergraduate real analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration and etc. 
An Introduction to the Theory of Numbers  
This free book, which presupposes familiarity only with the most elementary concepts of arithmetic is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. 
Group Theory  
Group Theory by Predrag Cvitanovic can be downloaded in pdf and postscript formats free of charge. 
