Learn Hardcore Chinese: wǒ men xiān zài túshūguǎn xuéxí, hòulái yìqǐ qù gōngyuán sànbù. - We first studied in the library, and later went to the park for a walk together.

先 = first / first of all / earlier (in sequence)
It comes before the verb phrase:
- 我们先在图书馆学习。
  We first study in the library.
后来 = afterwards / later on (in the past)
It is usually used when you are talking about past events from a later point in time:
- 我在北京工作，后来搬到上海。
  I worked in Beijing, later (on) moved to Shanghai.

Compare with 然后:

然后 = and then / after that (more neutral, can be past, present, or future)
In this sentence you could also say:
- 我们先在图书馆学习，然后一起去公园散步。
  This is very natural in everyday speech.
后来 often feels a bit more like a storytelling/past narrative link, especially when there is a clearer time gap.

So here, 先 … 后来 … presents a sequence of actions, and because 后来 often refers to what happened later (in the past), the whole sentence feels like a retelling of something that already happened.

Why is the word order 先在图书馆学习 and not 先学习在图书馆?

The core word order pattern in Mandarin is:

Subject + (Time) + (Manner) + (Location) + Verb (+ Object)

In this sentence:

Subject: 我们
Time/sequence adverb: 先
Location phrase: 在图书馆
Verb: 学习

So: 我们先在图书馆学习 is perfectly following that pattern.

About the alternatives:

✅ 我们先在图书馆学习。
Most natural and standard.
✅ 我们在图书馆先学习。
Also grammatical, but you slightly highlight "first in the library we study (as opposed to doing something else there)." This kind of word-order change is more about nuance and emphasis.
❌ 我们先学习在图书馆。
This is not natural. 学习 doesn’t normally take a following 在 + place phrase directly as its object. The location phrase with 在 comes before the verb (or at the very start of the sentence), not after it.

So: place introduced by 在 usually goes before the main verb phrase, not after it.

What exactly is 在 doing here? Is it a verb like "to be at" or a preposition like "in"?

In this sentence, 在 before 图书馆 functions like a preposition / coverb meaning at / in:

在图书馆 = at the library / in the library

It forms a location phrase:

在 + place

That phrase then modifies the action 学习 (to study):

我们先在图书馆学习。
We first study *in the library.*

Key points:

You cannot drop 在 here:
- ❌ 我们先图书馆学习 — not grammatical.
You can move the whole location phrase to the front:
- 在图书馆，我们先学习，后来一起去公园散步。
  In the library, we first study, then later go to the park for a walk together.

So here, think of 在 as a preposition introducing where the action happens.

There’s no past tense marker. How can I tell if this means "we studied" or "we will study"?

Chinese verbs usually do not change form for tense. Time is shown by:

Time words: 昨天 (yesterday), 明天 (tomorrow), etc.
Context (what the conversation is about).
Sometimes aspect markers like 了, 过, 着.

Your sentence by itself:

我们先在图书馆学习，后来一起去公园散步。

could, in isolation, be interpreted as:

Past: We first studied in the library, and later went to the park for a walk.
Future/plan: We’ll first study in the library, then later go to the park for a walk.

If you add time words, it becomes clear:

昨天我们先在图书馆学习，后来一起去公园散步。
Yesterday we first studied… then later went… (clearly past)
明天我们先在图书馆学习，后来一起去公园散步。
Tomorrow we’ll first study… then later go… (clearly future)

So you rely on time expressions and context, not on verb endings, to know the tense.

Why is 一起 placed before 去? Could I say 我们去公园一起散步 instead?

一起 means together and usually comes right before the main verb phrase it modifies.

Very natural patterns are:

我们一起去公园散步。
我们一起去公园散步。
我们在公园一起散步。

All of these mean roughly: We (will) go to the park for a walk together.

About 我们去公园一起散步:

It is grammatical and used, but the internal grouping is slightly different:
- 去公园 = go to the park
- 一起散步 = take a walk together
So the focus feels more like:
- We go to the park, and (there) we walk together.

For learners, the safest default is:

Subject + 一起 + (在 place) + Verb (+ Object)

e.g.
我们一起去公园散步。
我们在公园一起散步。

Why do we need both 去 and 散步 in 去公园散步? Why not just say one of them?

Each word contributes different information:

去 = to go (to) — movement from here to there
公园 = the destination (park)
散步 = the activity (take a walk / stroll)

So:

去公园散步 = go to the park to take a walk

If you only say:

我们去公园。
→ We go to the park. (You don’t say what for.)
我们在公园散步。
→ We take a walk in the park. (You don’t say whether you went there from somewhere else; it just describes being there and walking.)

去 + place + do-something is a very common pattern:

去超市买菜 — go to the supermarket to buy groceries
去朋友家玩 — go to a friend’s place to hang out

So 去公园散步 fits this same pattern: go to the park to take a walk.

What is the difference between 学 and 学习? Could the sentence use 学 instead?

学 and 学习 are closely related, and often interchangeable, but there are some tendencies:

学习
- Slightly more formal, often means to study in a broader sense.
- Very common in school/academic contexts.
- Often appears alone with no object:
  - 我在图书馆学习。 — I’m studying in the library.
学
- Slightly more colloquial in some uses.
- Very often used when you specify what you’re learning:
  - 学中文 — learn Chinese
  - 学钢琴 — learn piano

In your sentence:

我们先在图书馆学习
is perfectly natural and sounds like we first study (do our studying) in the library.

You could also say:

我们先在图书馆学习中文。
我们先在图书馆学中文。

Both are fine, with 学中文 being especially common in speech.

But 学习 on its own as to study is more common than just 学 on its own in this particular environment, so the original sentence is very natural.

What exactly does 散步 mean? How is it different from 走路?

Both involve walking, but the focus is different:

散步
- Means to take a walk / to stroll for relaxation or leisure.
- Typically no destination is emphasized; it’s about the activity itself.
- Example:
  - 晚饭后我们去公园散步。
    After dinner we go to the park for a walk (for pleasure).
走路
- Literally to walk / to go on foot.
- Focus is often on the way of getting somewhere, not on relaxing.
- Example:
  - 我每天走路去上班。
    I walk to work every day.

If you change the sentence to:

我们先在图书馆学习，后来一起去公园走路。

it’s understandable but sounds a bit odd; Chinese speakers strongly prefer 散步 for the idea of “go to the park for a walk (for fun).”

Should there be a 了 in this sentence to show completed actions?

You do not have to use 了 here. The sequence adverbs 先 and 后来 already make the order of events clear.

Current sentence:

我们先在图书馆学习，后来一起去公园散步。
→ Can describe a past sequence completely naturally, especially in context.

You can add 了 when you want to highlight completion or give more specifics:

我们先在图书馆学习了两个小时，后来一起去公园散步。
We first studied in the library for two hours, then later went to the park for a walk together.
后来我们一起去公园散步了。
Here, sentence-final 了 can mark a change of state or the realization of a plan:
Later we (finally) went to the park for a walk together.

But without 了, the sentence is still correct and quite natural. Chinese does not require a past marker the way English often requires past tense forms.

Why is 一 in 一起 pronounced yì and not yī?

The character 一 normally has first tone (yī), but its tone changes (tone sandhi) depending on what follows:

Before a 4th-tone syllable, 一 becomes 2nd tone (yí):
- 一个 — yí gè
- 一句 — yí jù
Before other tones, it usually becomes 4th tone (yì):
- 一起 — yìqǐ (3rd tone after it)
- 一年 — yìnián (2nd tone)
- 一般 — yìbān (1st tone)

So although dictionaries often list 一 as yī (1st tone), in natural speech you normally pronounce:

一起 → yìqǐ

The pinyin you see in the sentence (yìqǐ) already reflects this tone change.