I got my first cat!

Sleep (or pretend to sleep) in her vicinity. She’ll feel more comfortable to check you out and become more familiar with you. Just. Don’t. Move.

It’s bold of you to assume you own the cat. She owns you. You are her servant.

Jokes aside, my two oxytocin reactors love liquid snacks.

Be gentle and let her take her time to adjust. No sudden movements or loud noises. If she doesn't want to be touched then it's best to not touch her. She'll adjust eventually.

When I encounter a new cat, I offer my hand for a sniff, and if the cat acts scared or foes away, then I leave them alone. If they seem chill with it, I touch them a bit and see how they react.

I recommend reading or watching videos about cat body language. Also, remember treats and the slow blink!

Cats like the slow blink. When your looking at them and you make eye contact, slowly close your eyes, wait for a few seconds the slowly open them. Then avert your gaze.

As someone that's allergic i have noticed that the more I ignore them the more they love me, which is fine with me as long as I have my allergy meds.

What other posters said, respond with the blinking. My son calls them eye kisses. It shows trust. In case you're unfamiliar: you look at her and slowly close your eyes for a second. She might mirror it. Facing a fierce predator such as the one you pictured and confronting it willingly blinded, even for a second, takes courage. She'll honour it most likely. Also food and clean water, preferably placed in separate locations.

Don't try to move things along too quickly. Let her hide somewhere she feels safe until she's ready to come out. Give her nice food to eat and a clean litter tray. Let her come to you - don't try to stroke or hold her until she's ready for it. Learn basic cat language - narrowing your eyes and looking away is a sign of friendship. When she gets close enough, stroke the side of her face to show you like her. When you get closer, bumping noses is the cat equivalent of kissing.

Aside from what's already been said, you can try playing with her as well with toys that keep you at a distance from her. E.g. stick with a cord on it and some toy on the end of the cord or something similar.

Try just moving it around in front of her to get her interest, then let it stay still for 5-10s to see if she's interested in hunting it (if she goes flat on the ground, wiggles her butt or her head at it she's preparing to pounce). Don't let her get it easily but let her catch it before the end of playtime.

Some cats will appreciate it more than food, others won't - they each have their preferences.

If she doesn't engage and doesn't seem to be interested in the toy at all, just let her be.

I don't have a lot of experience with cats specifically, but pets need time to get used to a new home. This can take up to three months.

If this is day one, give them some space, blink slowly at them; let them know you're gentle and there if needed.

OMG She is realy cute, give her snack from me!

I've always had a lot of success with holding out my hand towards the cat, palm down, limp, and allowing the cat to inspect it in their own time.

I've heard this is also a technique from experts, but I just found it when we had a cat. It seems to work on dogs too.

It's non-threatening, and it doesn't put any pressure on them for a response. Just get it close enough to be just outside their personal space. If they stretch their nose towards it to sniff, you can bring it closer, and then you may just get the coveted nose bump and cheek nuzzle.

You may also get the, "what are you doing, you freak, leave me alone" body language, in which case you just have to wait and try again later.

Welcome to servitude. And you'll like it, or else...