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In the lecture Professor Narlikar presents non-standard cosmology that differs from the Big Bang model of the universe. Why standard Big Bang cosmology is unsatisfactory for Professor Narlikar? First of all, in this model the universe starts from space-timesingularity. This "edge of the universe" is hard to describe mathematically. Secondly, such model has many "epicycles", i.e. proposals added ad hoc in order to explain some observational phenomena. Those "epcicles" are, i.a., dark matter, dark energy or inflation. There is also some age problem -- some galaxies seem to be older than universe itself. Finally, this theory is highly speculative. In 1993 Professor Narlikar and his colleagues proposed so-called Quasi-Steady State Cosmology. In their model - instead of one Big Bang - there are plenty of micro-events that creates matter (initial minibangs). This way they avoid the problem with singularieties. The lecture contains many details, i.a. how microwave background is explained in their modelor which experimental data could refute their theory.