させてください details

causative

Examples

please let me do it — the speaker volunteers, or asks leave, for something they will do themselves

その仕事しごと、ぜひ私わたしにやらせてください。

sono shigoto, zehi watashi ni yarasete kudasai.

Please let me be the one to take that job on. neutral

ちょっと考かんがえさせて。明日あした返事へんじするから。

chotto kangaesasete. ashita henji suru kara.

Let me think about it — I'll give you an answer tomorrow. casual

すみません、明日あしたは少すこし早はやく帰かえらせてください。

sumimasen, ashita wa sukoshi hayaku kaerasete kudasai.

Sorry — please let me leave a little early tomorrow. neutral

本日ほんじつは体調たいちょうが優すぐれませんので、早退そうたいさせていただけませんか。

honjitsu wa taichou ga suguremasen node, soutai sasete itadakemasen ka.

I'm not feeling well today — might I be allowed to leave early? formal

する-verbs take the suppletive させる straight onto the noun —
紹介しょうかいさせてください, never ×紹介しょうかいしさせて — and 来くる
goes 来こさせてください.

させてもらう
させてもらう announces the speaker is going ahead as though consent were already in hand (説明せつめいさせてもらいます); させてください puts the permission genuinely on the table, so the listener is being asked and can still say no.

てください
The same ください, and the causative flips who does the work — 手伝てつだってください asks the LISTENER to act, 手伝てつだわせてください asks the listener to stand aside and let the SPEAKER act; drop the causative and the request comes out backwards.
させる
Bare させる has a causer who is not the speaker and reads as making or letting someone else act (子こどもに野菜やさいを食たべさせる); wrapped in ください the causer becomes the listener and the actor the speaker, which is what makes it a polite request rather than an order.