当たり前 is what needs no saying. Not true, not correct — unremarkable. Somebody keeps their word, the train runs on time, the lights come on: 当たり前. The word carries an assumption about shared standards, so it is only ever obvious to somebody, and most of the trouble learners have with it comes from forgetting that the speaker is the one deciding what counts as normal.
当然 is the same idea in a suit. It is the Sino-Japanese reading of the same first character, it belongs to writing, news and formal speech, and it works as a bare adverb the way 当たり前 cannot: 当然、責任を取ります, naturally I will take responsibility. 当たり前 is the native word and the spoken one — warmer, blunter, and much more likely to be said with feeling behind it.
もちろん answers a question; 当たり前 judges a situation. Asked whether you can help, もちろんです is a warm yes. 当たり前です is technically also yes, but it says obviously — why would you even ask, and to a customer or a senior colleague it lands as impatience. Between close friends 当たり前だろ is affectionate; almost nowhere else is.
The other half of the word is gratitude. 当たり前だと思っていた — I had been treating it as a given — and 当たり前じゃない — this is not a given — are how Japanese says the thing English says with “I took it for granted”. It is a common enough move that the phrase 当たり前の日常, ordinary everyday life, is almost always affectionate rather than dismissive.