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.
