에게 is used in writing. 친구에게 전화했다. I called my friend. 동생에게 선물을 줬다. I gave my younger brother/sister a gift. 너에게 실망했다. I was disappointed by you. 너에게서 희망을 보았다. I saw hope in you. 한테 is used in speech. 친구한테 갔었어. I've came to my friend. 동생한테 전화왔었어. I got a call from my younger brother/sister. (한테서 is the original form, 서 is left off.) 부터 since/from/first 며칠 전부터 잠을 제대로 못 잤어. I couldn't sleep well since a few days ago. 여기부터 시작하자. Let's start from here. 너부터 해. You do it first.

First, let us refer to some online dictionary webpages regarding the terms in concern: (Typical sample sentences may be found from the corresponding webpages.) 에　：http://www.google.co.kr/dictionary?langpair=ko|en&q=%EC%97%90 에게：http://www.google.co.kr/dictionary?langpair=ko|en&q=%EC%97%90%EA%B2%8C 부터：http://www.google.co.kr/dictionary?langpair=ko|en&q=%EB%B6%80%ED%84%B0 한테：http://www.google.co.kr/dictionary?langpair=ko|en&q=%ED%95%9C%ED%85%8C From there, it can be seen that, 1) 부터 is considered "from", "since" or "beginning with" in terms of a particular time period (it is similar to から or より in Japanese); 2) 에 is used for description regarding a position, a direction, and a time period (it is similar to に in Japanese); 3) 에게 and 한테 are quite similar (at least in my personal point of view), which is used to a person or to an object towards which an action performs (it is similar to に or へ in Japanese). There is also another term, 께, which is the honorific form of 에게. This means when an action performs towards a person who requires certain respect, 께 is adopted instead of 에게. Good day. / 좋은 일일 을.