  These highly informal lecture notes aim at introducing and explaining several
closely related problems on zeros of analytic functions defined by ordinary
differential equations and systems of such equations. The main incentive for
this study was its potential application to the tangential Hilbert 16th problem
on zeros of complete Abelian integrals.
  The exposition consists mostly of examples illustrating various phenomena
related to this problem. Sometimes these examples give an insight concerning
the proofs, though the complete exposition of the latter is mostly relegated to
separate expositions.
  For related and quoted articles, check the author's homepage
http://www.wisdom.weizmann.ac.il/~yakov .
