Black letter law is statutes, acts, regulations etcetera where the government has stated what the law is.
Case law arises from cases about the meaning of acts, regulations and also situations where there is no written law or the written law has missed out this problem. The inherent power of the court or of the government will always be case law.
Common law in the UK deals with situations where there was no legislation but judges had to make decisions. It notionally dates back to the 12th century.
Sometimes textbooks and legal articles are quoted in court to help the judge decide. A young barrister quoted to Lord Megarry from a textbook Megarry had written. Megarry's answer was "I rather think that passage will be revised in the next edition."