This chart is a list of the TV anime series that aired between July and September of 2013, along with their Laconic descriptions.
See Spring 2013 Anime for the previous season and Fall 2013 Anime for the season after that.
Here is the season's forum discussion.
TV Series:

- Blood Lad
(PV)
Airing from July 7 for 10 episodes
The adventures of an otaku ruler of Hell, as he tries to resurrect a Japanese schoolgirl he's fallen for.

- Brothers Conflict
(PV)
Airing from July 2 for 13 episodes
A girl finds herself with eleven brothers.

- Danganronpa: The Animation
(PV)
Airing from July 4 for 13 episodes
An Anime of the Game, based off the popular murder mystery Visual Novel about talented high school students who are locked within their own academy and are forced to murder each other and then discern who the culprit is all the while their own lives are at stake.

- The Eccentric Family (Uchouten Kazoku)
(PV)
Airing from July 7
About the life of a family of tanuki, in a world where youkai live openly.

- Fantasista Doll
(PV)
Airing from July 6
About dolls (that appear to be female humans) that fight and power up with cards.

- Fate/kaleid liner PRISMA☆ILLYA
(PV) (PV 2
) (PV 3
)
Streaming from July 6, airing from July 12 for 10 episodes
An AU of Fate/stay night, where Illyasviel Von Einzbern becomes a Magical Girl.

- Free!
(PV) (PV 2
)
Airing from July 3
A Sports Story by Kyoto Animation, focusing on an all-male swim team. Expect the Female Gaze to be rampant.

- Futari wa Milky Holmes
Airing from July 13th
Third season of Tantei Opera Milky Holmes, featuring two new characters. Nothing to do with Futari wa Pretty Cure.

- Gatchaman Crowds
Airing from July 12 for 12 episodes
A new series for the classic anime. Has an original plot, including a female lead.

- Gen'ei o Kakeru Taiyō a.k.a il sole penetra le illusioni (The Sun Penetrates the Illusions)
(PV)
Airing from July 6
An Anime First Magical Girl Warrior series. The premise is that 'Diabolos Tarot' feed on the souls of those without sin, countered by girls using the power of the 'Elemental Tarot'.

- Genshiken Nidaime
Airing from July 6
Despite what the title may have you think, this is the 3rd season of the anime.

- Hakkenden: Eight Dogs of the East 2
Airing from July 7 for 13 episodes
A continuation of the Winter 2013 Anime.

- High School D×D New
(PV)
Airing from July 7
Second season.

- Hyperdimension Neptunia the Animation
(PV) (PV 2
)
Airing from July 12
An anime of the popular game series featuring the 7th generation of video game consoles and video game companies as cute girls.

- Dog & Scissors
(PV)
Airing from July 1
A boy is killed and resurrected as a dachshund, now owned by a sadistic novelist that tortures him with scissors.
- Kanetsugu to Keiji
Airing from July 2
Another series about samurai in the Sengoku Period.

- Kimi no Iru Machi (A Town Where You Live)
(CM)
Airing from July 13
A boy living in the countryside suddenly has a girl from Tokyo move in with him.

- Kingdom 2
Airing from June 8 for 39 episodes
Second season.

- Kitakubu Katsudō Kiroku (Chronicles of the Going Home Club)
Airing from July 4 for 12 episodes
Slice of Life Schoolgirl Series, this time about a literal 'going home club'.

- Kiniro Mosaic (Golden Mosaic)
(PV)
Airing from July 6 for 12 episodes
A Japanese girl who'd spent time in Britain has the girl who she'd lived with while in Britain come to Japan.

- Love Lab
(CM)
Airing from July 4
Another Schoolgirl Series based on a yonkoma. This one involves a pair of girls practicing romance with each other.

- Makai Ouji: Devils and Realist (Hell Prince: Devils and Realist)
(PV)
Airing from July 7
An Impoverished Patrician accidentally summons a demon and discovers that he is qualified to choose the acting ruler of the demon realm.

- Monogatari Series Second Season
Airing from July 6 for 2 cours
Animated by Studio Shaft, a 2-cours adaptation of the six light novels that make up the middle third of the Monogatari series.

- No Matter How I Look at It, It's You Guys' Fault I'm Not Popular!
(PV)
Airing from July 8
A Cringe Comedy about a creepy otaku girl trying to become sociable and popular.

- Recorder and Randsell Mi
Airing from July 8
Third season

- Ro-Kyu-Bu! SS
Airing from July 5
Second season of elementary schoolers playing basketball.

- Rozen Maiden: Zurückspulen
(PV)
Airing from July 4
Third season. Based on the reboot manga.

- Senki Zesshou Symphogear G
Airing from July 4
Second season.

- Senyuu. Dai 2-ki
(PV)
Airing from July 2
2nd season of the Winter 2013 Anime

- Servant × Service
(PV)
Airing from July 4
Slice of Life comedy about public servants. From the creator of Wagnaria!!.

- Silver Spoon
(PV)
Airing from July 11 for 11 episodes
A City Mouse enrolls in a rural agricultural school, thinking it'll be an easy way to stay at the top of the class.

- Sunday Without God (Kami-sama no Inai Nichiyoubi)
(PV)
Airing from July 6
In a World where humans neither give birth nor die, a young girl that looks after them has the village under her care slaughtered by a man she then decides to follow.

- Tamayura ~More Aggressive~
(PV)
Airing from July 3 for 12 episodes
Second season of the healing Slice of Life anime.
- Teekyu 2
Airing from July 7
Second season

- Tokurei Sochi Dantai Stella Jogakuin Koutouka C³-Bu (Special Measures Unit: Stella Girls' Academy High School's C3 Club)
Airing fom July 4
A Schoolgirl Series, this time focusing on survival games (the fun kind, not the deadly kind).

- The World God Only Knows Megami-hen
Airing from July 8
Third season