This book is essentially selfcontained and requires only a basic abstract algebra course as background. The book includes and extends much of the classical theory of \(SL(2)\) representations of groups. Readers will find \(SL(2)\)Representations of Finitely Presented Groups relevant to geometric theory of three dimensional manifolds, representations of infinite groups, and invariant theory. Features ...  A new finitely computable invariant \(H[\pi ]\) associated to groups and used to study the \(SL(2)\) representations of \(\pi\).
 Invariant theory and knot theory related through \(SL(2)\) representations of knot groups.
Readership Researchers in invariant theory, representation theory of infinite groups, and applications of group representation theory to low dimensional topology. Reviews "A useful algebraic framework for students and researchers concerned with representation spaces. Apart from the contribution it offers to the algebraic insight in the topic it should be helpful especially for topologists who look at knots or 3manifolds from the CullerShalen perspective ... the monographis of considerable merit."  Zentralblatt MATH Table of Contents  The definition and some basic properties of the algebra \(H[\pi ]\)
 A decomposition of the algebra \(H[\pi ]\) when \(\frac 12\in k\)
 Structure of the algebra \(H[\pi ]\) for twogenerator groups
 Absolutely irreducible \(SL(2)\) representations of twogenerator groups
 Further identities in the algebra \(H[\pi ]\) when \(\frac 12\in k\)
 Structure of \(H^+[\pi _n]\) for free groups \(\pi _n\)
 Quaternion algebra localizations of \(H[\pi ]\) and absolutely irreducible \(SL(2)\) representations
 Algebrogeometric interpretation of \(SL(2)\) representations of groups
 The universal matrix representation of the algebra \(H[\pi ]\)
 Some knot invariants derived from the algebra \(H[\pi ]\)
 Appendix A
 Appendix B
 References
