UCLA Extension offers courses this fall--from one-day sessions to full-quarter classes--for animal aficionados of all kinds. Fundamentals of Horse Care, on Oct. 18, from 9 a.m. to 4 p.m., at L.A. Pierce College, Woodland Hills ($45). Horsemanship, an English-style riding class, on Oct. 1, from 7:30 to 9:30 p.m., at UCLA, then beginning Oct. 22, eight 1 1/2-hour riding sessions at Westlake Stables, Westlake Village ($155). Field Studies of California Birds, five Wednesday meetings beginning Oct. 8, from 7 to 9:30 p.m., at UCLA, and four Saturday field trips ($250). Tracking the Black Bear: A Weekend in Sequoia National Park, from Oct. 11 to 13 ($165 plus travel, meals and accommodations). Observing Animals: Behavioral Studies in Zoos, 12 Monday meetings, Sept. 22 to Dec. 15, from 7:30 to 10 p.m., plus observational training session on Nov. 1, at the L.A. Zoo Education Center ($135 for credit; $105 for noncredit). The World of Primates, five Wednesday meetings from Nov. 5 to Dec. 3, from 7 to 10 p.m., and one meeting Nov. 29, 9:30 a.m. to noon, at the L.A. Zoo Education Center ($115). For more information, call (213) 825-7093.