This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R, C}, two Banach spaces U and V over K, an open subset ? ? K, andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (?, L(U, V)) (1) for some r? N, such that L(? )? Fred (U,...