We know you have tons of free time at this university. No homework, right? Cadenza has the solution for you. Over 40 television shows are premiering this week, both new and returning, and we wanted to preview some of the most prominent ones for you. (And yes, we know you have no free time; That’s why we’re being helpful by only describing some of the shows.)

Monday

How I Met Your Mother – CBS, 7 p.m.
We might not yet know “How I Met Your Mother,” or who your mother is, but we now know where I met your mother. Ted meets the mother when he’s the best man at Barney’s wedding, a little ways down the road. Meanwhile, Ted just broke up with failed mother candidate number God-knows-how-many, and it’s getting a little harder to really care about Ted’s love life. Barney, on the other hand, is poised for the second serious relationship of his life with Nora, which leads to an inevitable love triangle when Robin realizes that she still has feelings for him. Barney also deals with a continuing struggle to reconnect with his estranged father, and, apparently, with a wedding. Lily and Marshall are pregnant, which is bound to make the whole gang start thinking more seriously about the future. All in favor of changing the title to “How Barney Met His Wife,” please say aye.

Castle – ABC, 9 p.m.
The season finale was fast-paced, heart-pounding and tear-inducing. One plot point to remember: Captain Montgomery, who had been involved with Beckett’s mother’s murder, was killed via gunshot. Beckett was shot at Montgomery’s funeral, and Castle was immediately by her side, begging her to stay with him and telling her that he loves her. In season four, the new captain will bring several changes to the station. Penny Johnson Jerald, from “24” and “Star Trek: Deep Space Nine” will be stepping in to fill Captain Montgomery’s shoes. She’s not happy with Castle’s constant presence, and she’s really not happy about his pseudo-relationship with Beckett. However, Castle’s declaration of love was a big deal. Tune in to see how Beckett and Castle’s relationship grows over the course of the season.

The Playboy Club – NBC, Monday, 9 p.m.
It’s yet another television show trying to shamelessly cash in on the “Mad Men” hype, but this one has Playmates. “The Playboy Club” takes place in 1963 at the first Playboy Club in Chicago. Amber Heard (“Pineapple Express”) stars as a newly hired Bunny; She has to deal with disrespectful men and compete with her fellow coworkers to pick up a rich husband. Despite its premise, “The Playboy Club” won’t be nearly as risqué as it would have you believe, because (a) Hugh Hefner has final say on the script, and (b) it’s on NBC.

Tuesday

Glee – FOX, 7 p.m.
“Glee” is back with what is sure to be another fabulous season of singing, dancing and drama. Over the summer, Blaine (Darren Criss) and Mike Chang (Harry Shum, Jr.) were promoted to series regulars, meaning that we’re sure to see more of them both. Blaine might even transfer to McKinley High. Chord Overstreet was not offered a regular role on the series as Sam Evans. He was offered the same guest contract he had last season but decided not to return to the show. This season will see some of the characters—namely Rachel (Lea Michele), Finn (Cory Monteith) and Kurt (Chris Colfer)—graduate, though whether or not they’ll leave the show after graduation has yet to be decided. Also, the winners of this summer’s “The Glee Project” reality show will be making their debuts this season. With so many cast changes, “Glee” will definitely surprise and maybe even entertain.

New Girl – FOX, 8 p.m.
Zooey Deschanel as Jess Day in FOX’s “New Girl” is truly “adorkable.” The plot centers around Jess, who, following a bad breakup, moves into an apartment with three single guys—Schmidt, Coach and Nick. As they get to know each other (and each other’s quirks), they begin to form a sort of family. One fun element is the Douchebag Jar— every time Schmidt makes a douchebag comment, he must put a dollar in the jar. This comedy offers an original view on relationships that is likely to keep viewers coming back for more. It’s relatable and funny, and Jess is easy to root for.

Unforgettable – CBS, 9 p.m.
Think you’ve seen enough police procedurals with ridiculous premises and even more ridiculous show titles? CBS doesn’t seem to think so. “Unforgettable,” which was formerly and hilariously called “The Rememberer,” stars Poppy Montgomery as New York City police detective Carrie Wells. Carrie suffers from hyperthymesia, a medical condition that causes her to remember everything. See what they did with the title there? The overarching story follows Carrie as she tries to find out how her sister was murdered. Intrigued? Neither am I.

Wednesday

The X-Factor – FOX, Wednesday and Thursday, 7 p.m.
After a season away from “American Idol,” Simon Cowell returns to television with an imported talent show from his native U.K. It’s essentially the simple weekly singing competition of “Idol” plus the mentorship of “The Voice,” except Simon was doing it way before “The Voice” even existed, so it’s way cooler. And Christina Aguilera isn’t a judge, which is good news for everyone. The other thing that sets “The X-Factor” apart is its four different categories: boys, girls, over-25s and groups. Joining Cowell at the judges’ table are Paula Abdul, L.A. Reid (former Island Def Jam chairman) and Nicole Scherzinger (of the Pussycat Dolls). Hopefully, the winning artists they choose are more Carrie Underwood than Lee “This guy won?” DeWyze.

Modern Family – ABC, 8 p.m.
Over the last two seasons, “Modern Family” has established itself as a force to be reckoned within the world of television. After winning an Emmy in 2010 for Outstanding Comedy Series, the show has become known for its wit and mockumentary-style “interviews.” The second-season finale, “The One That Got Away,” was full of the same jokes that are in every other episode, but that’s why it worked—Jay’s plans for a quiet birthday were shattered when Mitchell and Claire were cornered in a tree house by an angry dog in their old backyard; Phil convinced his high school rival that he’s married to Gloria; and Cam, after a phone conversation with Manny gets taken out of context, gets kicked out of a bakery and has to call Jay to pick up his own birthday cake. Viewers can expect Cam and Mitchell’s decision to adopt another baby and Haley’s and Alex’s respective senior and freshman years to be focal points throughout the new season, while the first few episodes will take place at a dude ranch, of all places.

Revenge – ABC, 9 p.m.
“Brothers and Sisters” may be gone from the ABC lineup, but new show “Revenge” brings back two of its crucial elements: the family drama and Emily VanCamp. In what looks to be a crime-drama-meets-family-drama, “Revenge” follows Emily Thorne (Emily VanCamp), who loses her father, decides it wasn’t an accident and starts to seek revenge. She moves to the Hamptons in order to infiltrate the community and destroy those who wrecked her own family years ago. “Revenge” also stars Connor Paolo (“Gossip Girl”), Gabriel Mann (“The Bourne Identity”) and Madeleine Stowe (“We Were Soldiers”) and promises to be another scandalous and dramatic addition to ABC’s fall lineup.

Law and Order: SVU – NBC, 9 p.m.
The pained cries of millions of vaginas echoed across the nation this summer when the producers of “Law and Order: Special Victims Unit” (commonly abbreviated as “SVU”) announced that Christopher Meloni, who plays dreamsicle detective Elliot Stabler, would not be returning for the show’s thirteenth season. Olivia Benson (Mariska Hargitay) will return, but her character’s screen time will be severely reduced mid-season. There are, however, a few glowing coals in the pile of “SVU’s” ashes. Two new characters, played by the ever-talented Danny Pino and Kelli Giddish, arrive in the season premiere. Pino’s detective Nick Amaro is Benson’s new partner and Giddish plays detective Amanda Rollins. Also, some old faces are set to come back—Stephanie March’s ADA Alexandra Cabot will return for at least a few episodes.

See Cadenza on Thursday for the rest of our TV preview coverage.