Beginning of past events
（刚）开始的时候：at the very start
Less formal, emphasizes the very beginning of the event
刚开始的时候，我觉得很内向。
Gāng kāishǐ de shíhou, wǒ juéde hěn nèixiàng.
At the beginning, I felt very introverted.
最初：at first, originally, initially
我最初的反应是害怕。
Wǒ zuìchū de fǎnyìng shì hàipà.
起先：at first, in the beginning
起先，我不同意这个想法。
Wǒ zuìchū de fǎnyìng shì hàipà.
起初：originally, at first, at the outset
Sequential order of past events
以后：after, later, afterwards, following, later on, in the future
Indicates a point after a point in time/a period after a period of time, can be used alone or after some time phrase (五年以后、毕业以后) OR just means in the future
上大学以前，我们以为大学生很轻松。上大学以后，我们才发现了大学生活每天都很忙。
Shàng dàxué yǐqián, wǒmen yǐwéi dàxuéshēng hěn qīngsōng. Shàng dàxué yǐhòu, wǒmen cái fāxiànle dàxué shēnghuó měitiān dū hěn máng.
从那以后：since then
从那以后，他们成了无话不谈的好朋友。
Cóng nà yǐhòu, tāmen chéng liǎo wú huà bù tán de hǎo péngyǒu.
此后：after this, afterwards, hereafter
Means 从这以后 but more formal
此后，两个人失去了联系，再也没见过面。
Cǐhòu, liǎng gèrén shīqùle liánxì, zài yě méi jiànguò miàn.
然后：after, then, afterwards, after that
Indicates an act that happens after a certain act or a certain condition. It is often used along with 先 to show the sequence of events
昨天我先去银行取钱，然后去书店买了三本书。
后来：afterwards, later
Only refers to the past, used on its own
我和我女朋友是大学同班同学，后来我出国了，所以我们就断了联系。
Wǒ hé wǒ nǚpéngyǒu shì dàxué tóngbān tóngxué, hòulái wǒ chūguóle, suǒyǐ wǒmen jiù duànle liánxì.
于是：thereupon, consequently, thus, hence
Goes at the beginning of a second clause (after a first clause) connecting two events in succession, where the first clause is the cause of the second. It often interchangeable with 所以 but not always because of the requirement of succession!
昨天你没有来，于是我就自己去餐厅吃饭了。
Zuótiān nǐ méiyǒu lái, yúshì wǒ jiù zìjǐ qù cāntīng chīfàn le.
接着：subsequently, after that
Also used at the beginning of a second clause, indicates the clauses usually share the same subject
最后：finally
Last event in terms of time/sequence
他考了两年大学都没考上，最后去了一家工厂当工人。
Tā kǎole liǎng nián dàxué dōu méi kǎo shàng, zuìhòu qùle yì jiā gōngchǎng dāng gōngrén.
终于：at last, in the end, finally, eventually
Indicates an expected situation/result (usually positive) that occurs after some kind of change
她经过一年的努力，终于考上了全国一流大学。
Tā jīngguò yì nián de nǔlì, zhōngyú kǎo shàngle quánguó yì liú dàxué.
Showing immediacy between actions/events
（刚）一······就······：as soon as
Connector before two verbs
她一回家就开始做作业。
Tā yì huí jiā jiù kāishǐ zuò zuo yè.
不一会儿、不久、不多时：before long
不一会儿 is less formal than the others
我先查了一下电子邮件。不一会儿，我房东的电话就来了。
Wǒ xiān chá le yíxià diànzǐ yóujiàn. Bù yíhuìr, wǒ fángdōng de diànhuà jiù lái le.
很快：very soon
一开始，我觉得这部电影没有意思。很快，我就改变主意了。
Yì kāishǐ, wǒ juédé zhè bù diànyǐng méiyǒu yìsi. Hěn kuài, wǒ jiù gǎibiàn zhǔyì le.
顿时：immediately, at once
Only used for past events
刚一进大厅，我们顿时就感到一种紧张气氛。
Gāng yí jìn dàtīng, wǒmen dùnshí jiù gǎndào yì zhǒng jǐnzhāng qìfēn.
马上：in the near future, right away, soon
Used for past or future, often used in imperatives
马上就要期中考试了，我得抓紧时间学习。
Mǎshàng jiù yào qízhōng kǎoshì le, wǒ de zhuājǐn shíjiān xuéxí.
突然、忽然：suddenly
妈妈突然感动地哭了起来。
Māma túrán gǎndòng de kū le qǐlái.
Other useful words
（有）一天：one day
那天：that day
那天，我们正在考试。 忽然，一个人跑了进来，大声说：“着火了！”
Nèitiān, wǒmen zhèngzài kǎoshì. Hūrán, yíge rén pǎole jìnlái, dàshēng shuō:“Zháohuǒle!”
正在、正、呢：used to show progressive mood
妈妈给我打电话时，我正在睡觉。
Māma gěi wǒ dǎ diànhuà shí, wǒ zhèngzài shuìjiào.
这时、这个时候、此时：right now, this moment
这时 is short for 这个时候, and 此时 is more formal
去年这个时候，我还是个学生呢，现在已经成了一名老师了。
Qùnián zhège shíhou, wǒ háishì ge xuésheng ne, xiànzài yǐjīng chéngle yì míng lǎoshī le.
同时：in the meantime, meanwhile
我在给她电话的同时，她也在给我打电话。
Wǒ zài gěi tā diànhuà de tóngshí, tā yě zài gěi wǒ dǎ diànhuà.
一边······一边······：simultaneously
Means you are doing two things at the same time
爸爸常常一边开车，一边打电话。
Bàba chángcháng yì biān kāichē, yì biān dǎ diànhuà.
等······再：wait until…then
他们打算等雨停了再走。
Tāmen dǎsuàn děng yǔ tíng le zài zǒu.
等······才：wait until…only then
他们等雨停了才走。
Tāmen děng yǔ tíng le cái zǒu.