rectification; Abhyankar-Sathaye embedding problem; variable monodromy theory; isolated singularities; critical points; Picard-Lefschetz theory; Gauss-Manin connection; Picard-Fuchs systems; oscillating integrals; abelian integrals; Hodge structures; period mappings; regular and irregular singularities; Riemann-Hilbert problem; isomonodromic deformations; holomorphic foliations; differential Galois theory; hypergeometric functions 