MANDOLIN:
There are so many wonderful websites for learning the mandolin. Some of my favorites:
Artistworks Mandolin Lessons: Three of the best mandolinists on the planet Mike Marshall (all styles), Caterina Lichtenberg (classical), and Sierra Hull (bluegrass) each provides a series of lessons from beginner to advanced. One of the amazing things about Artistworks lessons is that you can submit videos of your playing to your teacher and s/he will provide a video response. Almost like having face-to-face lessons! There are some free lessons to get a taste then subscription-based, and well worth it!
Peghead Nation Mandolin Lessons: Wonderful style-based lesson series featuring great mandolin players teaching bluegrass, old-time, new compositions, Irish, choro, swing, etc! from beginning to advanced. John Reischman, Sharon Gilchrist, Marla Fibish, Mike Compton, Joe K. Walsh, Aaron Weinstein, Ian Coury, Ethan Setiawan, and Chad Manning. I have had the fortune of participating in workshops with many of these folks and you will benefit greatly. Also subscription-based.
Patreon: Many generous teachers giving so much time to creating wonderful content for mandolin learners. Some that I have benefited from are (excellent players all): David Benedict, many great lessons plus a series of in-depth interviews with other well-known mandolinists, Jake Howard, well-done lessons with lots of transcriptions, Martin Hayes, expert Irish fiddler teaching many tunes by ear step-by-step (while not mandolin, same tuning and amazing music that you can take to an Irish session!), Chris Haigh (The Fiddle Channel), again not mandolin per se but lots of transcriptions and tunes well-presented. And of course many, many more. If you find you have learned a lot from someone, please support them by subscribing!
MUSIC THEORY:
http://www.teoria.com/
Great website for beginning music theory and ear-training. In Spanish or English. Donate if you can, they deserve it!
http://www.musictheory.net
Excellent website with theory lessons, trainers for ear-training, note, scale and chord identification, chord calculator, staff paper generator, even a matrix generator for twelve tone pieces. And a note, interval, scale, and chord identifiers for fretboards including mandolin! I highly recommend their two apps as well.
http://randscullard.com/CircleOfFifths/
Very cool interactive online version of the Circle of Fifths.
http://www.good-ear.com/
Online Ear-Training Website
http://www.looknohands.com/chordhouse/
Chords and Scales for Piano and Guitar
http://www.musicards.net/
Flash cards for note names, key signatures, intervals, triads, etc. Does not keep score but great for drilling your skills (if you’re honest!).
http://www.gmajormusictheory.org/Fundamentals/workbooks.html
Free Music Theory Workbooks for beginning fundamentals/theory.