Andersen was a prolific Danish author born in the early 19th century. He gained lasting fame from his fairy tales intended for children (his first volume of fairy tales was published in 1835) although some were based on traditional tales, others were original or only loosely based on the source material. Like the works of the brothers Grimm, Andersens tales are often retold and abridged so make sure you get a complete translation. Here are a few examples (not comprehensive) of where it can be sourced, I have tried to link directly to the relevant web page on a site where possible.
Online Books-Full electronic copies of facsimiles of editions Andersen’s Fairy Tales can be found free online here are examples from the Internet Archive and Google Books
Online Booksellers-for example Amazon, Abe Books
Library-For example North Yorkshire Libraries
Book shops-(you may have to order), you could try finding an independent local bookshop in your area