Explore advanced asymptotic methods in mathematics through this lecture by Don Zagier, part of the SISSA/IGAP/SUSTech series on "Standard and less standard asymptotic methods." Delve into techniques for evaluating infinite sums numerically and recognizing asymptotic patterns in number sequences. Learn both standard approaches like the Euler-Maclaurin formula and less conventional methods, illustrated through diverse examples. Tackle challenging problems such as evaluating a slowly convergent sum to 250 decimal places, analyzing the asymptotic behavior of complex series coefficients, and computing highly oscillatory infinite series for large real numbers. Gain insights into powerful mathematical tools for handling complex numerical evaluations and asymptotic analysis across various branches of mathematics.