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In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Topology. --- Milnor fibration. --- Singularities (Mathematics) --- Fibering theorem, Milnor --- Fibers, Milnor --- Fibration, Milnor --- Milnor fibering theorem --- Milnor fibers --- Milnor fibres --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Mathematics. --- Algebraic geometry. --- Functions of complex variables. --- Algebraic topology. --- Several Complex Variables and Analytic Spaces. --- Algebraic Geometry. --- Algebraic Topology. --- Math --- Science --- Topology --- Complex variables --- Elliptic functions --- Functions of real variables --- Algebraic geometry --- Geometry, Algebraic --- Polyhedra --- Set theory --- Algebras, Linear --- Differential equations, partial. --- Geometry, algebraic. --- Partial differential equations