The sign & is known as the ampersand. Some distinguished writers have used it in print, among them G.B. Shaw and H.W. Fowler; but the first was always eccentric in his spellings and punctuation, while the second was writing a reference book and, it may be thought, trying to save space. When you are as distinguished as they were, you may use the ampersand if you wish. Till then, you should avoid it in formal writing. Certainly, it is frowned on in the presentation of academic writing.
It is of great use in one's private handwritten (or scribbled) notes. It is nowadays essentially a mark in handwriting, not in any form of print. It often takes the form of +, or some private version of it.
You may be interested to know where this word comes from.