또 and 다시 are synonyms; 또 is used in the sense of "repeatedly" somehow. 또 시작한다 It starts again (it had started and now it starts again). 다시 is used in the sense of "do it from the start". 다시 시작한다 It starts (from the start). 또 can express the speaker's mood as in "또 똑같은 문제가 생겼어! The exact same problem happened again!" 다시 is a neutral word in my opinion.

1) ~도 is attached to a noun, which means 'also.' 사과도 필요하고, 귤도 필요하고, 배도 필요하네. 2) 다시 is an adverb, which means 'again.' 다시 시작하자 드라마 다시 보고 있어.

steve, glad to hear about your korean wife :) 1. "도" or "두" "도" is "too" or "also". "두" is also "too" or "also". "두" is wrong in spelling i think, But many people use. :) It sounds Cute. :) eg) 나도 사과 먹고 싶어. I also want to eat apple. me too. 나도. 나두. 2. "또" and "다시" "또" is "다시". "또" is "again". "다시" is "again". eg) 다시 가자 go again. 나는 그 책을 다시 읽었어. 나는 그 책을 또 읽었어. I read the book again. 나는 그 책을 또 다시 읽었어. no need using both together "또" and "다시". But it makes more emphasis.

다시 has some other meaning differ from 또.. when you learn music intsrument like cello or violin.. when you play some part. and your teacher isn't satisfied then your teacher will say '다시 해보세요' . that means you'd check yourself what was wrong and play it better than before.. . or other case.. in office.. you report something but your boss don't like it and said '다시 해오세요'.. that means you should correct it and report again. in this case your teacher and your boss won't say '또 해보세요 or 또 해오세요..' because they don't want you do it sameway.. .... ... .. . and .. some other case.. when you learn cello but you are so busy to learn cello so you quit to learn it... and you'll say '언제 다시 첼로를 배울지 모르겠다. ' (i don't know when i can start to learn cello again).. 또 only means repeat... but in this case 다시 means you'll start again what you quit before..