Real-world uses of Algebraic Structures I am a Computer science student, and in discrete mathematics, I am learning about algebraic structures. In that I am having concepts like Group,semi-Groups etc...    
Previously I studied Graphs. I can see a excellent real world application for that. I strongly believe in future I can use many of that in my Coding Algorithms related to Graphics.
Could someone tell me real-world application for algebraic structures too...

The fact that electrons , positrons , quarks , neutrinos and other particles exist in the universe is due to the fact that the quantum state of these particles respects poincare invariance. Put in simpler terms, If Einstein's theory of relativity is to hold , Some arguments using group theory show that these kinds of particles that I mentioned respects Einstein's theory and that there's no fundamental reason they shouldn't exist. Scientists have used group theory to predict the existence of many particles .We use a special kind of groups called lie groups that are groups and manifolds in the same time.For example $GL(n,R)$ is a lie group of invertible linear transformation of the n-dimensional Euclidean space. Symmetry operations correspond to elements living inside groups. If you map these symmetry elements to the group of invertible (and Unitary) transformations of a Hilbert Space ( An infinite dimensional vector space where particle quantum state lives ) You can study how these particle states transforms under the action of the group
