You can gain muscle mass with calisthenics, though beyond a certain point it becomes much harder than using weights. As a beginner though you should be able to gain at least some mass no matter how you go about it.
Here are a list of some exercises to look up.
- Squats, though very quickly you will find these are too easy without additional weight.
- Split squats. These can be either a regular split squat, a lunge, or a Bulgarian split squat. These are quite a lot better than regular squats since you're putting all of your weight on one leg which helps increase the load.
- Jumps. These can be box jumps or tuck jumps. They tend to be better than squats because launching yourself into the air requires more power than just standing up.
- Glute bridges. Can also be done one leg at a time, good if you want to specifically target your glutes and hamstrings.
- Calf raises. These will likely be necessary if you don't want your upper legs to get way thicker than your lower legs, though jumps can work your calves well if you're making sure to engage them as you lift off the ground.
Some harder ones that you probably won't be able to do immediately:
- Pistol squats. Great exercise, impossible for beginners.
- Nordic curls. Great to target hamstrings. Unlike pistol squats you can make these easier by not going all the way down.
In general, if you can do more than 20 reps in a row ("can't" would mean you literally can't do another one, not it feels hard) then you need to find a way to make it harder. Often this might mean adding weight of some kind, or modifying the exercise. If you can easily do 20 split squats for example it might be time to start training pistol squats.
You should think about which particular muscles you're hitting and make sure you're getting enough sets in to maximize muscle growth in all of them. In general this should be at least 3 and up to 6 sets of some combination of exercises which hit each muscle on any given day, and at least 12 sets per week.
You should rest each muscle at least every other day, you grow muscle while recovering from exercise not while doing it. Do not hit any muscle two days in a row, and get plenty of sleep. You probably want to train at least 2 days a week, and no more than 6. The sweet spot is most likely 3 days a week, but if you feel like you aren't getting any fatigue you can go more often.
Lastly make sure to eat a lot of protein, way more than you think. You cannot grow muscle if you don't give your body enough to build them. Body builders will typically aim for 1g of protein per lb of bodyweight, so for you that's 155g of protein per day. You absolutely will not be eating that much without making a specific effort to do so.
Note that the first week or two you are likely to have a lot of muscle soreness. If the muscle soreness doesn't settle down after 3 weeks you're probably going too hard and need to slow down a bit.
