Elevated levels of Lipoprotein(a) may also be classified as a form of hyperlipidemia. Familial (primary)
Familial hyperlipidemias are classified according to the Fredrickson classification, which is based on the pattern of lipoproteins on electrophoresis or ultracentrifugation. It was later adopted by the World Health Organization (WHO). It does not directly account for HDL, and it does not distinguish among the different genes that may be partially responsible for some of these conditions. Type I
Type I hyperlipoproteinemia exists in several forms:

Lipoprotein lipase deficiency (type Ia), due to a deficiency of lipoprotein lipase (LPL) or altered apolipoprotein C2, resulting in elevated chylomicrons, the particles that transfer fatty acids from the digestive tract to the liver
Familial apoprotein CII deficiency (type Ib), a condition caused by a lack of lipoprotein lipase activator. : 533 
Chylomicronemia due to circulating inhibitor of lipoprotein lipase (type Ic)Type I hyperlipoproteinemia usually presents in childhood with eruptive xanthomata and abdominal colic. Complications include retinal vein occlusion, acute pancreatitis, steatosis, and organomegaly, and lipemia retinalis. Type II
Hyperlipoproteinemia type II is further classified into types IIa and IIb, depending mainly on whether elevation in the triglyceride level occurs in addition to LDL cholesterol. Type IIa
This may be sporadic (due to dietary factors), polygenic, or truly familial as a result of a mutation either in the LDL receptor gene on chromosome 19 (0.2% of the population) or the ApoB gene (0.2%). The familial form is characterized by tendon xanthoma, xanthelasma, and premature cardiovascular disease.
Remnant hyperlipidemia occurs as a result of abnormal function of the ApoE receptor, which is normally required for clearance of chylomicron remnants and IDL from the circulation. The receptor defect causes levels of chylomicron remnants and IDL to be higher than normal in the blood stream. The receptor defect is an autosomal recessive mutation or polymorphism. Type IV
Familial hypertriglyceridemia is an autosomal dominant condition occurring in approximately 1% of the population.This form is due to high triglyceride level. Other lipoprotein levels are normal or increased a little.Treatment include diet control, fibrates and niacins. Statins are not better than fibrates when lowering triglyceride levels. Type V
Hyperlipoproteinemia type V, also known as mixed hyperlipoproteinemia familial or mixed hyperlipidemia, is very similar to type I, but with high VLDL in addition to chylomicrons. It is also associated with glucose intolerance and hyperuricemia.In medicine, combined hyperlipidemia (or -aemia) (also known as "multiple-type hyperlipoproteinemia") is a commonly occurring form of hypercholesterolemia (elevated cholesterol levels) characterized by increased LDL and triglyceride concentrations, often accompanied by decreased HDL. On lipoprotein electrophoresis (a test now rarely performed) it shows as a hyperlipoproteinemia type IIB. It is the most common inherited lipid disorder, occurring in about one in 200 persons. In fact, almost one in five individuals who develop coronary heart disease before the age of 60 has this disorder. The elevated triglyceride levels (>5 mmol/L) are generally due to an increase in very low density lipoprotein (VLDL), a class of lipoprotein prone to cause atherosclerosis.