Another is used where you would expect "an other", so for example "The child got an iPhone. The other child got an iPhone too." "I'd like to go to a place. I'd like to go to another place." Neither means something like "also not". It is used in conversation such as: A: "I don't like mathematics." B: "Neither do I." Neither could be seen as a short form of "not either". Either does not have the negative part to it. you could have a conversation like this: A: "I don't like mathematics." B: "I do not like it either." Here you have to say the "not", so that's how it differs from neither. I don't expect you to understand it right away. Perhaps try to look up a few sentences with another, either, neither and see if you can spot the pattern that I'm trying to show you.

Other: Different thing/things (use it on its own or with 'any' in front). It can refer to singular or plural, so like "In other words" or "On the other hand", "If this was any other time I would be delighted" Another: A different thing but less personal, so an alternative to "My other" or your "Your other" etc but something you don't own. Just 'other' can also be impersonal, but unlike "another" it can also refer to one's own different thing. "My other wallet is black" "Another wallet I've seen is black" (not anyone's in particular; just a different one) Either: Means: "One of those". "Either my flashlight is broken, or it just needs new batteries" (it is one of these two possibilities) Neither: Like "either", but none of the possibilities are true, so "My flashlight is neither broken nor needs new batteries; it's just too light in this room to see it". "Neither of them saw the ghost" (Not one of them saw the ghost) Another thing helpful to know: "nor" is often paired with "neither", it basically means "or" but negative. You could say: "I'm not leaving a tip or even paying for these drinks", as the word "not" shows the negative part of the sentence so you can use "or". However, you could also say the same but with nor, in which you'd say: "I'm neither leaving a tip nor paying for these drinks".