Primary structure: Amino acids (AAs), the building blocks for all proteins, are linked together by peptide bonds. The primary sequence tells you the AAs in the protein but not the 3D shape.
Secondary structure: Hydrogen bonding between the H2N- of one AA and COO- of the adjacent AA to increase stability. The two structures that can be formed include the alpha helix and the beta pleated sheet.
Tertiary structure: The polypeptide forms a 3D shapes. It is made up of multiple secondary structures which are held together by ionic bonds between amino acids, further hydrogen bonds, Van der Waal dispersion forces (temporary fluctuating dipoles in the hydrocarbon groups of the AAs) and disulphide bridges (between two cysteine AAs).
Quarternary structure: Multiple polypeptides join to form a protein e.g. in haemoglobin (oxygen carrying protein in the blood), the haem group is formed from 4 polypeptide chains.