A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving. This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewriting and unification. The completeness and soundness of the ?RP-calculus, sort theorem, and automated theorem prover for the ?RP-calculus are also elaborated. This publication is a good source for students and researchers interested in many-sorted calculus.