Core: Yes. There are yoga poses to target just about every core muscle. Want to tighten those love handles? Then prop yourself up on one arm and do a side plank. To really burn out the middle of your abs, you can do boat pose, in which you balance on your "sit bones" (the bony prominences at the base of your pelvic bones) and hold your legs up in the air.
The first Hindu teacher to actively advocate and disseminate aspects of yoga, not including asanas, to a western audience, Swami Vivekananda, toured Europe and the United States in the 1890s. The reception which Swami Vivekananda received built on the active interest of intellectuals, in particular the New England Transcendentalists, among them Ralph Waldo Emerson (1803–1882), who drew on German Romanticism and philosophers and scholars like G. W. F. Hegel (1770–1831), the brothers August Wilhelm Schlegel (1767–1845) and Karl Wilhelm Friedrich Schlegel (1772–1829), Max Mueller (1823–1900), Arthur Schopenhauer (1788–1860), and others who had (to varying degrees) interests in things Indian.