粒子物理学の標準モデル

Standard model of particle physics標準モデル1. Similar to periodic table of elements2. Lie groups U, LU, mean what3. Symmetries mean what?4. Fields mean what?5. Why are some fields defined as left-handed?
Lie groups seem to be distinct from Lie algebras, but I am unsure how.
A Lie group seems to be a group that corresponds to a differentiable manifold. It also corresponds to a map from (x,y) to xy^(-1). I am not sur ehow these two items are correlated. Lastly, it seems that a Lie group can be related to the "Eight-Fold Way" of particle physics.
Wikipedia says:
リー群（リーぐん、Lie group）は群構造を持つ可微分多様体で...