How do you win over a tennis lover?

ask her to give you the lessons

Does your university had mixed couples teams?

My wife and I were in a similar boat in college. I was a tennis hacker who loved to play (not quite where you are) and she was an accomplished tennis player (star of her high school team from 8th grade on.) First some warnings: You don't want to get hyper competitive with someone you're dating. You're out there for fun and you're likely outclassed anyway, so no cursing, throwing rackets, trash talking. I've seen couples play together where I cringe with discomfort watching them on the court, even when they are on the same team. Not everyone can suppress their competitive fires enough to spare their partner when something goes wrong and partnerships where there is a significant skill mismatch produces lots of tension.

That said, definitely learn to play. Go out, have a good time, try your hardest and understand that she will thump you good. She should be in a good mood to go out afterward and you will be the butt of good natured stories. Play some mixed, but get an understanding ahead of time. Some people play mixed for the social aspect and some play to win. You need to know what you're doing. Mixed is a place where a guy can get a bad reputation quickly. Two things to watch for to see if you can keep it up: If the stories aren't good natured, that's a really bad sign. If you manage to win a set and she gets angry, that's another bad sign.

You should get the Battle of the Sexes video from the early 70's where Billie Jean King whips Bobby Riggs arrogant ass. She will love you.

I don't know, have to think about it re your circumstances.

I was not bad in my beginning tennis lessons at the university, but still with no idea of spin or anything like that, just trying to hit the ball, and, some time later, was asked out by a music/physics major.. who happened to play tennis at a fairly high college level. I'd never played doubles before, was a complete flub up. The date went well..

It didn't really matter, we were sort of even on smarts and stupidities.

In tennis some terms used regularly are:
love
match
ready position
set
serve
receiver
grand slam
frame

Try your best ,the result is not so that important .

Cave man style - hit her over the head with a tennis racket and drag her off to the locker room. She'll thank you for it.

Why do you feel that you have to whoo this gal over with tennis?
That's "her thing" - let it be.
Instead, find something cool to do together. Find another common ground.
My husband had his golf; I was out on the boat. At the end of the day we had lots to talk about and each felt there was something to bring to the other person.

PS don't wait until next Fall to approach this gal! Do it now.