表示“进入（某场所）、入学”等义时，enter 后面不用 into，例如：She entered the room quickly. 她悄悄地进入屋中。/ He entered university at the age of 21.他21岁时进入大学。/I entered this this company five years ago. 我5年前进入这家公司。/ She wouldn't enter our conversation.我们在谈话，她不想插一脚。（摘自外研社、建宏《英汉多功能词典》）

   表示“开始（工作、交涉等），处理（问题等），缔结（协定等）”的意思时，用 enter into , 例如：He entered into an argument with the teacher.他和那位老师争论。 / enter into a contract with a firm 和公司订立合同 （摘自外研社、建宏《英汉多功能词典》）

Definition of enter into phrasal verb from the Oxford Advanced Learner's Dictionary

enter into：phrasal verb

enter into something

 (formal)

1. to begin to discuss or deal with something

   Let's not enter into details at this stage.

2. to take an active part in something

   They entered into the spirit of the occasion (= began to enjoy and feel part of it).

3. [no passive] to form part of something or have an influence on something

   This possibility never entered into our calculations.

   Your personal feelings shouldn't enter into this at all.

enter into something (with somebody)

to begin something or become involved in something

to enter into an agreement

to enter into negotiations

(1)enter 后面接具体空间位置场所，不需要加介词into。因为enter +地点名词=go into +地点名词

He entered the room briskly and stood near the door. 

他轻快地走进屋里，站在门边。

Before entering the bathroom, he emptied his dirty laundry into the hamper. 

进浴室前，他把脏衣服全都放进洗衣筐里。

(2)enter into +名词+with sb加入（讨论）;订立（协议）;开始（关系）

I have not entered into any financial agreements with them.  

我还没有和他们订立任何财务协定。

We entered into meaningful discussions with them weeks ago.

几周前，我们和他们进行了意义深远的讨论。

(3)enter into +名词成为…的一部分；成为…的一个因素；构成

There were also other factors that entered into the orchestration.  

管弦乐编曲还要考虑其他因素。