What should I pack for summer in Europe?

I would definitely pack gear for rainy weather. Europe can be dreary at times, but it can also be fierce. Much of my time in Berlin was spent with a raincoat in my bag, just in case it struck while I was out. Since it's the summer, it's bound to get hot too. I made sure I had a few pairs of shorts, one good pair of jeans, and dresses. Dresses are easy to pack because they aren't bulky, giving you more room for other things in your suitcase, like a few good pairs of walking shoes. If I were you, I'd ditch bringing blow dryers, curling irons, etc. I brought one thinking I would use it but ended up letting it air dry most days because it seemed like such an unnecessary hassle. Definitely keep minimal as you'll be walking most places, sweating in whatever you wear.
My roommate only brought a carry-on sized bag and a backpack for our 4-week stay. I challenge you to do the same!

For summer, dresses are great. They are a full outfit and don't take up a lot of room in your suitcase. Plus, at least in Italy where I studied, there are a lot of bathrooms that are not the easiest to use and wearing a dress can definitely help with the ease of squatting over a literal hole in the ground behind a door (which is actually how the bathrooms actually are in some places!)

Definitely forget all of the hair styling products and equipment. If you are going in the summer and have long hair, you'll probably wear your hair up most of the time anyway.

Rain gear and a sweater or two are definitely a must but just remember that you can wear the same sweater for literally days in a row. I packed two sweaters for four months and wore them all the time. All students in my program had to do the same thing so we were all in it together!

Sneakers and hiking boots saved my feet, but sandals are also good too!

As far as underwear and socks, pack as much as you can in crevices and pockets of your suitcases. If you run out of clean underwear, it's a lot worse than running out of clean shirts or pants.

Finally, I really liked having pictures of my family and friends from home to look at every now and then so slip those anywhere you can!

Bring clothes that you can layer or wear as a lot of different outfits. One top can be made into four or five outfits depending on what you wear it with and how you accessorize. A white t-shirt and a handful of scarves won't take up a lot of space, and creates a few cute outfits! Shoes tend to take up the most space, so I would recommend bringing shoes for many different activities. Some that you can wear in the rain or hiking are always a good idea, and if you can get one pair of boots for both that's best. And if you're worried about clothes smelling or getting dirty - stuff dryer sheets in your bag. They keep your things smelling fresh and as a bonus, they ward off bugs!