Explore advanced asymptotic methods in mathematics through this comprehensive lecture series. Delve into techniques for evaluating infinite sums and recognizing asymptotic laws of numerical sequences. Learn both standard approaches like the Euler-Maclaurin formula and less conventional methods, illustrated with numerous examples. Tackle challenging problems such as evaluating slowly convergent sums to high precision, analyzing asymptotic behavior of complex sequences, and computing highly oscillatory series. Gain insights into power series, smooth and divergent series, numerical computations, and special values. Investigate intriguing mathematical phenomena like Euler's mysterious formula and the Basel problem. Develop skills in time management, order analysis, and rough asymptotics while exploring the philosophical aspects of mathematical inquiry.