Q:
What are the anagrams and their varieties?

A:
An anagram is the rearrangement of the letters of a word, name, phrase, sentence, title, or the like into another word or phrase. ALL the letters of the name or phrase must be used ONCE and only ONCE. This is the basic rule of anagramming. The best anagrams are meaningful and relate in some way to the original subject. They can be apposite, funny, rude, satirical or flattering.

AMBIGRAM: An ambigram is an art form that may be read as one or more words not only in its form as presented, but also from another viewpoint, direction, or orientation. The words readable in the other viewpoint, direction or orientation may be the same or different from the original words.
ANIGRAM or ANIMAGRAM: Anagram showing the letters of a word or phrase moving as they rearrange to form an anagram. 
ANTIGRAM: An anagram which is antonymous of the original phrase, such as Mother-in-law = Woman Hitler
PANGRAM: These are anagrams of the alphabet, e.g. abcdefghijklmnopqrstuvwxyz.
SYNANAGRAM: Single words that are anagrams of other single words, Tread = Rated
TRIANAGRAM: Also called triplets, these are three-way anagrams such as Admires = Sidearm = Misread.

Some of the interesting sentences that include the phrases as also their anagrams can be experienced at this link.