I am trying to learn about the various SU groups related to QCD. I have about 5 QFT and Particle physics books from my student library and written down about 20 pages of handwritten notes about specific parts of say generators, matrices, group properties etc. - but i dont really feel that I understand the deeper connection between all this. Can someone (preferably) in simple words and not too many equations, explain what relevant SU symmetries connect QCD and HOW? To me it seems impossible to get a feeling of the big picture here. I feel that when i zoom in on a specific part it gets somewhat clear, but i need to understand the bigger picture. I am specifically interested in the connection between chiral symmetry - the left/right-handedness breakdown to vector/axial symmetry - what is happening here? I can understand that this can be done in SU(2) handeling only u and d quarks - or SU(3) handeling u, d, and s quarks. One is a better approximation than the other - again why? How does this relate to the 8 Goldstone bosons (3 pions, 3 kaons, 2 eta) emerging when going from SU(3)_L x SU(3)_R to only SU(3)_V The same can be said for the SU(2) "version" of this, where the breakdown gives rise to 3 Goldstone bosons (the 3 pions). I know that theory says they need to be massless, but how do we then use it as a legit model strong interactions? i have read on the linear sigma model, eightfold way, chiral symmetry transformations, rotational transformations, gauge invariance among many things. What i really want is to connect some of the ideas. I know i am asking an extremely broad question, so feel free to choose any smaller domain you would like :-) Thank you very much!