P.D. Magnus 
Forallx – An Introduction to Formal Logic [EPUB ebook] 

Forallx is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. This book treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven.
Contents:
What is logic?
Sentential logic
Truth tables
Quanti ed logic
Formal semantics
Proofs
Other symbolic notation
Solutions to selected exercises