For what it's worth, I've been a hobby gunsmith for 25 yrs. Don't waste your time with the correspondence courses. I took the Penn course and the North American School of Firearms course (no longer in business). They are garbage. I also have the AGI Professional Gunsmithing Course.
The AGI course has a lot of good information but it is poorly filmed & produced. The instructor Mr. Dunlap is very knowledgable but also very lazy (as far as the course is concerned that is). I say "lazy" because many times in the videos he tries to explain the function of a firearm but decides it would be too much trouble to take the gun or assembly apart. He gives you a lot of detailed information on how to fix various types of firearms but he rarely shows you how to actually do it. He uses a chalk board to explain certain parts relationships and uses cut-away guns when possible. His favorite teaching tool seems to be his hands !! He will attempt to explain a function by using his hands instead of taking apart the gun in question that is sitting right in front of him !! The course was filmed in analog format back in 1992. The quality is lacking and the camera operator seems to be asleep at times because he misses the close-up shots that the instructor is trying to point out !! It is really annoying. Also, the AGI course is not for complete novices. There are a lot of terms, tools and procedures mentioned that they assume you are already familiar with.
To sum it up, the mail order courses are a waste of money. The AGI course has a lot of very good design, function & repair information but it is presented in a half-hearted way in my opinion. I can best describe it this way: It's like having a gunsmith read you a very good gun repair book with video pictures. This course sells for close to $4000 and if you want to learn machining, welding and heat treatment, it will cost quite a few thousand extra on top of that $4000. Much too expensive for what you actually get and you will be far from a "certified gunsmith" after viewing 108 hours of video. If you can buy the course used on ebay for a reasonable price, go for it. In my opinion a person aspiring to be a real gunsmith should attend a certified gunsmith school and/or apprentice under an experienced gunsmith.