If you only learn about two things in rheumatology (which you probably will), do: Rheumatoid arthritis and osteoarthritis. These are by far the most important conditions in rheumatology, and can cause back pain, a common complaint. There are a whole host of types of inflammatory arthritis, so you should probably have a wee look at them too!
Other things that bother rheumatologists are gout and pseudogout. Septic arthritis is important as it is an infection of the joint. Finally, the spondyloarthropathies are a group of not particularly fun conditions.
Connective tissue diseases
So let's get it out of the way systemic lupus erythematosus (SLE), lupus or magic House disease is a connective tissue disease. Sarcoidosis is another connective tissue disease which, much like magic House disease, has approximately 250,473 different clinical features. Finally, systemic sclerosis, which consists of scleroderma and vasculitis is an inflammation of blood vessels (which are kind of connective tissue. Kind of.
Polymyositis and dermatomyositis are forms of muscle inflammation. Fibromyalgia is a chronic pain syndrome, usually a diagnosis of exclusion. Polymyalgia rheumatica (PMR) is a chronic form of muscle inflammation, also a diagnosis of exclusion.