〜ていく

go on / go (doing)

Adds movement away from the speaker, in space or in time: "do and go", "take along", or a change that continues from now into the future.

Readings

How to form it

Put the verb in the て-form and add いく. いく conjugates like 行(い)く and is usually written in hiragana.
Taking something along, or doing something before you go: お弁当(べんとう)を持(も)っていく (take a packed lunch).
Movement away from the speaker: 鳥(とり)が飛(と)んでいった (the bird flew away).
An action or change continuing from now on: これからも勉強(べんきょう)していきます (I'll keep on studying).

これからも日本語(にほんご)を勉強(べんきょう)していきます。

I'll keep studying Japanese from now on.

お弁当(べんとう)を持(も)っていく。

I'll take a packed lunch with me.

〜てくるcome (to) / start to
Movement toward the speaker, or a change that has built up to now.