This practical guide demonstrates the use of methods to analyze sequential data, from basic standard methods to advanced novel techniques, all in the setting of an accessible, intuitive view of underlying statistical theory. The book reveals the unappreciated limitations of standard methods and shows how simple new viewpoints can overcome these obstacles and open up novel opportunities for discovery. Readers, from beginning students of astronomy, physics, statistics, and other technical subjects, to seasoned practitioners in these fields, are invited to use thought-provoking exercises to delve deeper into important topics without resorting to mindless calculations. Several case studies are included - not only to point out the end results, but to illustrate how the scientific process is actually carried out in practice. Scargle, a well-known pioneer in the field, shares his decades of experience to demonstrate improvements and extensions of classical techniques and discourage uncritical use of 'black box' analyses.