There are many metabolic pathways/cycles/processes/reactions that are involved in the synthesis or degradation of carbohydrates and compounds formed from them. Please note that most of these pathways aren't specific to carbohydrates only. Gluconeogenesis will be covered in the protein section, because amino acids are a common substrate used for synthesizing glucose.
-synthesis of glucose from a non-carbohydrate source
-breakdown of glucose to pyruvate
-conversion of pyruvate to acetyl-CoA
Citric Acid (Tricarboxylic acid (TCA), Kreb's) Cycle
-acetyl-CoA combines with oxaloacetate to form citrate; ATP, NADH, and FADH2 are produced in the cycle
Electron Transport Chain
-oxidative phosphorylation, producing ATP from NADH and FADH2