Per a l'excursió, he de pujar la muntanya i després baixar al riu.

Per a l'excursió gives the context or purpose: for the hike / for the excursion.

In Catalan, per a often expresses:

• purpose
• destination
• intended use

So here it means something like as part of the hike or for the hike.

A learner may also notice that in real-life Catalan, especially in some varieties, the difference between per and per a is not always kept very strictly in everyday speech. But in careful standard usage, per a is a good choice here.

Catalan often drops the vowel of the article before a word that begins with a vowel or silent h.

So:

• la + excursió becomes l'excursió

This is called elision.

Other examples:

• l'escola
• l'amiga
• l'hora

It works much like French, and a bit like contractions in English, though it is more systematic in Catalan.

He de means I have to or I must.

It comes from the verb haver used in the structure:

haver de + infinitive = to have to / must

So:

• he de pujar = I have to climb / go up
• he de baixar = I have to go down

A very important point: he here is not the English pronoun he. It is a Catalan verb form meaning I have in this structure.

You may also hear haig de instead of he de in some varieties of Catalan. Both are used.

In Catalan, pujar can be used transitively, meaning to go up / climb something directly.

So:

• pujar la muntanya = to climb the mountain

English often uses climb the mountain, so this may feel natural. But if you were thinking in terms of go up, you might expect a preposition. Catalan does not need one here.

Compare:

• pujar la muntanya = climb the mountain
• pujar a la muntanya = go up to the mountain / go up onto the mountain area

So the version in your sentence focuses on the mountain as the thing being ascended.

Here baixar al riu means go down to the river.

That a is important because the river is the destination.

So:

• baixar al riu = go down to the river

By contrast, baixar el riu usually means something more like:

• go down the river
• travel downstream along the river

So the difference is:

• baixar al riu → movement to the river
• baixar el riu → movement along/down the river

This is a very useful distinction.

Al is the contraction of:

• a + el = al

So:

• al riu = to the river

This is mandatory in normal Catalan.

Other common contractions:

• del = de + el
• als = a + els
• dels = de + els

So baixar al riu literally contains a el riu, but that must become al riu.

Catalan often uses definite articles more readily than English, especially when talking about something specific or understood in context.

Here:

• la muntanya = the mountain
• el riu = the river

This suggests that the speaker has a particular mountain and river in mind, probably the ones involved in the hike.

If the meaning were less specific, Catalan could use an indefinite article:

• una muntanya
• un riu

But in your sentence, the definite articles sound natural because the route seems known.

Després means afterwards, then, or later.

In your sentence:

• i després baixar al riu = and then go down to the river

Yes, it can often move around a bit, depending on style and emphasis. For example:

• Per a l'excursió, he de pujar la muntanya i després baixar al riu.
• Per a l'excursió, he de pujar la muntanya i baixar després al riu.

The first version is more natural and neutral.

Catalan word order is fairly flexible, but not completely free. Després usually goes where it clearly modifies the sequence of actions.

With he de + infinitive, the sentence mainly expresses obligation, necessity, or something the speaker feels is required.

So it is closer to:

• I have to climb the mountain and then go down to the river

rather than simply:

• I will climb the mountain and then go down to the river

That said, in real life, obligation can sometimes overlap with planned itinerary. For example, if this is the route of the hike, he de may sound like that’s what I’m supposed to do.

Yes. Many learners notice both forms.

Both of these are used:

• he de
• haig de

They both mean I have to.

Very broadly:

• he de is standard and widely accepted
• haig de is also common in many spoken varieties

So a learner should recognize both. If you use he de, you are absolutely safe in standard Catalan.

Not exactly. These verbs are broader than the most literal English equivalents.

• pujar can mean go up, climb, ascend
• baixar can mean go down, descend, come down

So the best English translation depends on context.

Examples:

• pujar les escales = go up the stairs
• pujar la muntanya = climb the mountain
• baixar del cotxe = get out of the car / get down from the car
• baixar al riu = go down to the river

This flexibility is very normal in Catalan.