If you really are all for learning Elvish, there are two possible choices for you:SindarinQuenyaBoth are Elvish languages that have extensive online courses for you.But, if you want to learn Tengwar, the Elvish writing system along with it, this format isn't going to work for you, so, get the PDF file by going to google.com and typing in 'Pedin Edhellen' (the name for the Sindarin course), and clicking [PDF] on the result that says 'Pedin Edhellen a Sindarin course'.Both Pedin Edhellen and Quetin i Lambe Eldaiva are written by Thorsten Renk, one of the most reliable Elvish language teachers that I know of.
Yes, actually there is this type of writting called "Tengwar", used and created by Tolkien. There is also the Feanorian script, and a lengthy list of words in the back of the Silmarillion. In theory it would be possible to read and speak elvish, but although a brilliant creation, it is not a fully functioning language(s). See the Appendixes to the Lord of the Rings, the Silmarillion, and the Histories of Middle-earth for more information.But, if you wish to not just learn the writing system, but actually learn one of the Elvish languages (Sindarin or Quenya), then there are many online, free-to-download courses online. Try Pedin Edhellen for Sindarin, or Quetin i Lambe Eldaiva for Quenya.