Glycolysis literally means "splitting sugars." Glucose, a six carbon sugar, is split into two molecules of a three carbon sugar. In the process, two molecules of ATP, two molecules of pyruvic acid and two "high energy" electron carrying molecules of NADH are produced. Glycolysis can occur with or without oxygen. In the presence of oxygen, glycolysis is the first stage of cellular respiration. Without oxygen, glycolysis allows cells to make small amounts of ATP. This process is called fermentation.
The Citric Acid Cycle:
The Citric Acid Cycle or Krebs Cycle begins after the two molecules of the three carbon sugar produced in glycolysis are converted to a slightly different compound (acetyl CoA). Through a series of intermediate steps, several compounds capable of storing "high energy" electrons are produced along with two ATP molecules. These compounds, known as nicotinamide adenine dinucleotide (NAD) and flavin adenine dinucleotide (FAD), are reduced in the process. These reduced forms carry the "high energy" electrons to the next stage. The Citric Acid Cycle occurs only when oxygen is present but it doesn't use oxygen directly.
Electron Transport requires oxygen directly. The electron transport "chain" is a series of electron carriers in the membrane of the mitochondria in eukaryotic cells. Through a series of reactions, the "high energy" electrons are passed to oxygen. In the process, a gradient is formed, and ultimately ATP is produced.
Maximum ATP Yields:
In summary, prokaryotic cells can yield a maximum of 38 ATP molecules while eukaryotic cells can yield a maximum of 36. In eukaryotic cells, the NADH molecules produced in glycolysis pass through the mitochondrial membrane, which "costs" two ATP molecules.