Preface; Part I. Singularities at Infinity of Polynomial Functions: 1. Regularity conditions at infinity; 2. Detecting atypical values via singularities at infinity; 3. Local and global fibrations; 4. Families of complex polynomials; 5. Topology of a family and contact structures; Part II. The Impact of Global Polar Varieties: 6. Polar invariants and topology of affine varieties; 7. Relative polar curves and families of affine hypersurfaces; 8. Monodromy of polynomials; Part III. Vanishing Cycles of Non-Generic Pencils: 9. Topology of meromorphic functions; 10. Slicing by pencils of hypersurfaces; 11. Higher Zariski-Lefschetz theorems; Notes; References; Bibliography; Appendix 1. Stratified singularities; Appendix 2. Hints to exercises; Index.