This book offers a concise introduction to both proof-theory and algebraic methods the core of
the syntactic and semantic study of logic respectively. The importance of combining these two
has been increasingly recognized in recent years. It highlights the contrasts between the deep
concrete results using the former and the general abstract ones using the latter. Covering
modal logics many-valued logics superintuitionistic and substructural logics together with
their algebraic semantics the book also provides an introduction to nonclassical logic for
undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in
Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut
elimination and its applications in detail. It also provides simplified proof of cut
elimination making the topic more accessible. The last chapter of Part I is devoted to
clarification of the classes of logics that are discussed in the second part. Part II focuses
on algebraic semantics for these logics. At the same time it is a gentle introduction to the
basics of algebraic logic and universal algebra with many examples of their applications in
logic. Part II can be read independently of Part I with only minimum knowledge required and
as such is suitable as a textbook for short introductory courses on algebra in logic.
