We will discuss Lefschetz pencils and will prove Lefschetz's theorem on hyperplane sections (without using transcendental methods), which will give us a more or less full understanding of the (co)homology of nonsingular complex algebraic varieties up to the middle dimension. Time permitting we will also discuss the Picard Lefschetz monodromy formulas and sketch a proof that will follow roughly the same lines as our proof of the weak Lefschetz theorem.