ている、ていく、てくる、ては、ても

ている (te-iru)

iru = existing

Use ている

Progressive tense – currently doing
Continuous – have been doing
Present situation – what do you do now?
Habitual actions – frequently happens
The current state / State / condition / appearance of subject

Examples for ている

見る (miru) to look; to watch
見ている (mite iru) looking; watching; seeing

読む (yomu) to read
読んでいる (yonde iru) reading

ていく(te-iku)

iku = go, start
(alternatively ゆく, it's less conversational)

Use ていく

to start; to continue; to go on

Examples for ていく

歩いていく (aruite iku) to walk / to go by walking / to start walking

てくる (te-kuru)

kuru = come

Use てくる

to do… and come back; to become; to continue; to start

Examples for てくる

見えてくる (miete kuru) to come into view (to continue coming into view)
私は彼を連れてくる。(watashi wa kare o tsurete kuru.) I will bring him / pick him up.

ては / では (te-wa / de-wa)

Use ては / では

if; because + bad result
whenever [A] happens, [B]..
multiple repetitive actions

Examples for ては / では

こんなに雨が降っては、買い物ができないな。(konna ni ame ga futte wa, kaimono ga dekinai na.) I can't go shopping if it keeps raining like this.
彼が相手では勝てるわけがない。(kare ga aite de wa kateru wake ga nai.) If he is my opponent, there is no way I can win.

ても (te-mo)

Use ても

even; even if; even though

Examples for ても

たくさん食べても、お腹が空きます。(takusan tabetemo, onaka ga sukimasu.) Even if I eat a lot, I still feel hungry.
日曜日でも、働きます。(nichiyoubi demo, hatarakimasu.) I work even on Sundays.