What do you mean, "the universe"? By many standard theories of cosmology, the universe is infinite, so of course the number of stars is also infinite. Even if it's not infinite, it's probably vastly larger than we can see or ever hope to see.
But if you just count the observable universe, which is the part of the universe lying within the cosmic particle horizon, close enough to us that light has had time to reach us since the Big Bang (and due to the expansion of the universe, the cosmic particle horizon is further away from us than simply "age of universe * speed of light"), there are about `10^24` stars, one septillion. ("septillion" sounds made up, but it isn't, except in the way that all words are ultimately made up.)
This is so many stars that if you lined them all up in a cube, that cube would be 100 million stars across; assuming an average diameter of 1 million kilometers, even if the stars were somehow touching each other the cube would still be 100 trillion kilometers wide, meaning that if our sun were in the center, the cube wouldn't actually fit between us and the nearest stars which are about 40 trillion kilometers away.