Explore advanced asymptotic methods in mathematics through this lecture from the SISSA/IGAP/SUSTech series on "Standard and less standard asymptotic methods." Delve into techniques for evaluating infinite sums numerically, guessing exact values, and recognizing asymptotic laws of number sequences. Learn both standard approaches like the Euler-Maclaurin formula and less conventional methods, illustrated with numerous examples. Tackle challenging problems such as evaluating a slowly convergent sum to 250 decimal digits, expanding an infinite sum and analyzing its coefficients' asymptotic behavior, and computing a highly oscillatory series for large real numbers. Cover topics including plane partitions, interpolation techniques, knot invariants, domain growth, Richardson interpolation, closed formulas, and asymptotic tricks. Gain valuable insights into advanced mathematical problem-solving over the course of this 1 hour and 40 minute lecture.