تمارين التمدد بعد الإحماء وقبل تمارين التهدئة.

Because this is a phrase, not a full sentence with a finite verb. In Arabic, short instructional headings, labels, and schedule items often appear without a verb.

So this phrase works like:

• Stretching exercises after the warm-up and before cool-down exercises

It is very natural in Arabic to omit a verb in this kind of context.

تمارين means exercises.

Its singular is تمرين = exercise.

So:

• تمرين = one exercise
• تمارين = exercises

This is a broken plural, which means the plural is formed by changing the internal pattern of the word, not just by adding a suffix.

Because تمارين التمدد is an iḍāfa construction, often called a genitive/possessive construction.

It literally means:

• exercises of stretching

In an iḍāfa:

1. the first noun usually does not take ال
2. the second noun can be definite or indefinite
3. the whole phrase gets its definiteness from the second noun

So:

• تمارين التمدد = the stretching exercises / stretching exercises

You do not say التمارين التمدد in standard Arabic for this meaning.

التمدد means stretching.

It is a verbal noun / abstract noun, and in this phrase it acts like the second part of the iḍāfa:

• تمارين التمدد = stretching exercises
• literally: exercises of stretching

So التمدد is not an adjective here. It is a noun.

Because بعد and قبل mean after and before, and they are commonly used with nouns in Arabic.

Here:

• بعد الإحماء = after the warm-up
• قبل تمارين التهدئة = before the cool-down exercises

In grammar terms, بعد and قبل are often treated as adverbial nouns that behave much like prepositions in these expressions.

الإحماء means the warm-up or warming up.

It has ال because it refers to a specific known activity: the warm-up.

So:

• إحماء = warm-up / warming up
• الإحماء = the warm-up

In this phrase, the definite form sounds natural because we usually mean the specific warm-up phase in a workout or training routine.

التهدئة means cooling down, calming down, or the cool-down depending on context.

So:

• تمارين التهدئة = cool-down exercises
• literally: exercises of cooling down

It is parallel to تمارين التمدد:

• تمارين التمدد = stretching exercises
• تمارين التهدئة = cool-down exercises

Yes, that is possible, but the meaning shifts slightly.

• بعد الإحماء وقبل التهدئة = after the warm-up and before the cool-down
• بعد الإحماء وقبل تمارين التهدئة = after the warm-up and before the cool-down exercises

The version in your sentence is more specific because it refers to the exercises themselves, not just the cool-down phase in general.

و simply means and.

So the structure is:

• بعد الإحماء = after the warm-up
• وقبل تمارين التهدئة = and before the cool-down exercises

This connects the two time expressions:

• after X
• and before Y

Grammatically, in an iḍāfa construction, the whole phrase takes its definiteness from the second noun.

Since التمدد is definite because of ال, تمارين التمدد is also definite as a whole.

So literally it is closer to:

• the stretching exercises

But in English, depending on context, we often translate it more naturally as just:

• stretching exercises

Arabic and English do not always match perfectly in how definiteness is expressed.

A careful pronunciation in MSA would be approximately:

tamārīnu t-tamaddudi baʿda l-iḥmāʾi wa-qabla tamārīni t-tahdiʾati

In normal pausal pronunciation, learners often simplify it to something like:

tamāriin at-tamaddud baʿd al-iḥmāʾ wa-qabl tamāriin at-tahdiʾa

A few helpful notes:

• تمارين = tamārīn
• التمدد = at-tamaddud in connected pronunciation, because ت is a sun letter, so ل in ال assimilates
• الإحماء = al-iḥmāʾ
• التهدئة = at-tahdiʾa, again with assimilation because ت is a sun letter

Because in an iḍāfa construction, the second noun can absolutely be definite with ال.

In fact, that is very common.

Examples:

• كتاب الطالب = the student’s book
• تمارين التمدد = stretching exercises
• تمارين التهدئة = cool-down exercises

What you cannot usually do is put ال on the first noun of the iḍāfa in this kind of structure. So:

• تمارين التمدد = correct
• التمارين التمدد = not correct for this structure

It can be broken down like this:

• تمارين التمدد = stretching exercises
• بعد الإحماء = after the warm-up
• وقبل تمارين التهدئة = and before the cool-down exercises

So the full structure is:

• [noun phrase] + [time expression] + [time expression]

This is very typical of Arabic instructions, workout plans, schedules, and headings.