In 1918 Poland became again an independent country. This was a good point for a remarkable development of science. Great mathematical centres were created in Lwów (with Banach, Steinhaus and Mazur) and Warszawa (with Sierpiński, Mazurkiewicz and Kuratowski). Nevertheless, Kraków was also very important to Polish mathematics. Zaremba and Żorawski played the main role in mathematics at the Jagiellonian University. Several young outstanding mathematicians, educated in Kraków, joined mathematical staff at the Jagiellonian University, particularly Franciszek Leja, Tadeusz Ważewski, Witold Wilkosz and Stanisław Gołąb. Teaching mathematics appeared to be at remarkably high level. Mathematically, Kraków represented first of all mathematical analysis and related areas, especially differential equations, but several other advanced courses were also organized, for example on topology, geometry, number theory, algebra. In particular, there were courses on algebraic functions, Hilbert spaces and Riemann surfaces. Also, many topics concerning different applications of mathematics were lectured. Among mathematicians who delivered mathematical courses for shorter period of time were also Jerzy Spława-Neyman and Otton Nikodym. It should be notedthat before World War II the results of Kraków mathematicians were so respected in the mathematical world, that several of them were invited speakers at International Congresses of Mathematicians. Polish mathematics was struck very strongly during World War II. It was also the case of Kraków mathematicians.