1.engage的基本意思是“约定”,即凭借契约、誓言或诺言等约束人或事。用于约束别人,即表示“雇”“聘”; 用于约束自己,则表示“许诺”“保证”。这种允诺可信,有约束力,并将履行一段时间,如“订婚”等。引申可表示“占用,吸引,引起”或“使忙于,使从事”等。
2.engage主要用作及物动词,接名词、代词作宾语。作“雇,聘”解时可以接以as短语充当补足语的复合宾语。作“保证”解时可接for+名词或that从句,也可接oneself+to-v构成的复合结构。
3.engage接介词in可表示“参加”; 接介词with可表示“交战”; 表示“订婚”则接介词to。

engage for(v.+prep.)
允诺; 保证 promise; guarantee
▲engage for sth
I will engage for his behaviour should you decide to employ him.如果你能决定雇用他,那么我可以担保他的行为。
I can engage for his honesty.我保证他为人诚实。

engage in(v.+prep.)
参加; 从事; 忙于 make sb join with one in sth; busy oneself with
▲engage in sth
I have no time to engage in the debate.我没时间参加辩论。
He engaged in a serious study of the problem.他对这个问题进行了认真的研究。
▲be engaged in sth/v-ing
My family has been engaged in farming for generations.我家几代都从事农业。

engage to(v.+prep.)
订婚 be promised in marriage to sb
▲be engage to sb
He was engaged to my sister.他和我妹妹订婚了。
I am engaged to Mr. Worthing,mama.妈妈,我与沃森先生订婚了。

engage with(v.+prep.)
交战attack each other
▲engage with sb
Our ships have engaged with the enemy.我们的舰船已与敌人交战。

用作及物动词
▲S+～+n./pron.
He has engaged a new secretary.他已雇了一位新秘书。
I've engaged a room at the hotel.我已经在旅馆里预订了一个房间。
Bright colours engage a baby's attention.鲜艳的颜色引起婴孩的注意。
The spots of blood on the floor engaged the attention of the police.地板上的血迹引起了警察的注意。
Housework engages much of her time.家务事占用了她很多时间。
◇ 用于be ～ed 结构
Can you come on Sunday?No,I'm engaged.你星期日能来吗?不能,我已有约了。
Please wait a minute, he is engaged just now.请稍等一会儿,他正有事呢。
Tom and Mary are engaged.汤姆和玛丽订婚了。
Her attention was engaged by the display of new hats in the shop window.商店橱窗里展出的新式帽子吸引了她的注意力。
He is engaged at a bank.他受雇于一家银行。
The typist is engaged for a week on trial.那位打字员被试用一周。
▲S+～+that-clause
Can you engage that all his statements are trustworthy?你能担保他的话都可靠吗?
▲S+～+to-v
He engaged to read the book.他答应看这本书。
I will engage to be there on time.我保证准时到那儿。
The company had engaged to finish the building by May.公司保证大楼在5月份完工。
用作宾补动词
▲S+～+pron./n.+to-v
He engaged himself to pay back the money.他保证还钱。
She engaged herself to attend the meeting.她答应一定去参加会议。
◇ 用于be ～ed 结构
He was engaged to be married to her.他跟她订过婚。
▲S+～+n./pron.+as n.
He engaged Mary as a secretary.他聘玛丽当秘书。
Our department has engaged a foreign teacher as phonetic adviser.我们系已经聘请了一位外籍老师作为语音顾问。
◇ 用于be ～ed 结构
The old man was engaged as a guide.那位老人被雇用为向导。

engage, hire
参见hire条。

engage, contract, covenant, pledge, promise
参见promise条。

I'm engaged.可以理解为“我订婚了”,也可以理解为“我有事”,须根据上下文来确定。