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Enzymes (and all proteins for that matter) are made up of amino acids linked to each other through the peptide bond. The linear sequence of amino acids is known as the primary structure of the protein. The primary structure is encoded for through the DNA. If you took the enzyme, and stretched it out end to end while holding onto both ends (the C-terminus end and the N-terminus end), then you would have a polypeptide with only primary structure. This, of course, doesn't exist in the cell. No enzyme exhibiting only primary structure would ever work.
However, the primary structure is frequently folded into regular patterns like loops (helices) and sheets. These regular patterns of localized structure is known as secondary structure. All enzymes have secondary structure too. The two most common forms are the alpha-helix and the beta-pleated sheet. You can find pictures of these in most any textbook (Biology, Cell Biology, Biochemistry, etc.). A protein with primary and secondary structure only still wouldn't work.
All active and functional enzymes have what is called tertiary structure. Simply put, this is the complete three dimensional structure of the enzyme, with all of its twists and turns, coils and sheets, etc. all put together into one nice complex structure. So, one way to look at it is that the tertiary structure is made up of secondary structure which is made up of primary structure. Got it?
But, some (only some) enzymes also have another level of structure. How can an enzyme have more than a three dimensional shape, you ask? Well, it can't, ...
Enzymes are thoroughly exemplified.