Here are the history of origin of the problem, short review of works, formulating of purpose of the research and main results in form of theorems. We considered all asymptotic expansions of solutions to the sixth Painlev'e equation near all three its singular points x=0, x=1 and x=∞ for all values of its four complex parameters. They form all together 111 families and include expansions of four types: power, power-logarithmic, complicated and exotic. Most of these expansions are new.

Mathematical problems and theory of numerical methods