Aim for the Ace!

Aim for the Ace! (エースをねらえ!, Ēsu o Nerae!) is a classic Shoujo anime and manga begun in 1972. Highly influential to shoujo, it had several series throughout the 70's and 80's and a live-action movie in 2004. It has been dubbed and distributed in Europe, in French, Italian and Spanish.

The story focuses on Hiromi Oka, who is an ordinary high school girl whose one wish is to be as good at tennis as the girl who is best in the school, the graceful "Madame Butterfly" Reika Ryuuzaki. Her coach Jin Munakata sees potential in her, and the rest of the series tells of her struggles and victories, on and off the court.

There was also a 1979 animated movie, which has noticeably better animation (directed by Osamu Dezaki, who also directed Rose of Versailles)

Gunbuster starts out as an Affectionate Parody of this series before evolving into its own thing.

Tropes used in Aim for the Ace! include:

Adaptation Expansion: The last OVA series (appropriately subtitled "Final Stage") picks up where the manga ended and wraps up some loose ends, most importantly Hiromi's relationship with Toudou.
Alpha Bitch: Reika starts out acting like this, being the queen bee and at first angered that a newcomer like Hiromi could possibly have made the top five, but she warms up to her eventually.
Backstory: Jin's expands on why he wants his girls to be strong after training
Defrosting Ice Queen: Reika
Doorstopper: A 3000 page manga! Mostly because of its long running and popularity over many years.
Ending Theme: One of the earliest examples of the "mellower, sad ending tune" formula, "Shiroi Tennis Court"
Even the Girls Want Her: Reika
Hair Decorations: Reika's big pink bow, the team captain's white barrettes, and Kyoto's awful orange bow-buns.
Gaming and Sports Anime And Manga
Genki Girl: Hiromi
Love Bubbles: Happens when Reika's around.
Melodrama
Naive Newcomer: Both Hiromi and Maki. Maki was really just in it to goof around from the start.
The Ojou: Reika
Onee-Sama: Reika for Hiromi. The two eventually take on a doubles tournament as a team.
Passionate Sports Girl: Tennis is Hiromi's big passion, and she gives her all during matches.
Pastel-Chalked Freeze-Frame: Most notably in the 90-minute movie retelling, directed by famed Osamu Dezaki.
Princess Curls: Reika's long blonde ringlets allude to her Ojou upbringing.
Stock Shout Out: If you see the Princess Curls on a one-shot character in an anime, she'll end up playing tennis against that show's lead character.
The Stoic: Coach Jin
Training from Hell
To Be a Master: Perfectly exemplifies the Japanese attitude of doing your best in everything (ganbarimasu). Hiromi's aspiration to reach the same level as her Onee-Sama Reika is a major part of her character arc.