Mad Men (10 p.m., AMC) – The second half of the seventh and final season of “Mad Men” starts, with only seven precious episodes before it’s all over. After that, no more morose Don Draper, no more determined Peggy Olson, no more quick-quipping Roger Sterling, and no more undaunted Joan. The secrecy surrounding the show’s final seven episodes would confound Edward Snowden, so instead of wild conjecture about what’s ahead (Will Don die? Will Pete lose the rest of his hair?), perhaps it’s best to review where we left off, so that everyone’s ready tonight. (Spoilers ahead, for those who haven’t gotten through 7a.) In a nutshell: With Bert’s passing came some slick dealings by Roger to merge the company and save Don’s job; Peggy’s personal life is a mess, but she’s on a roll professionally after nailing the Burger Chef account; and Don and Megan are headed toward divorce, but she’s still in 7b promos, so don’t write her off yet. All we know about tonight’s episode is that Don attempts to track down a friend while Joan tries to solve a problem with an account.
Sinatra: All or Nothing at All (8 p.m., HBO) – In part 1 of this documentary about singer Frank Sinatra, Sinatra becomes a superstar, faces a mid-career decline and has an epic comeback that includes an Oscar win.