Este semestre tengo geografía los lunes y química los miércoles.

In Spanish, tener is very commonly used to talk about the classes or subjects you have on your schedule:

Tengo geografía los lunes = I have geography on Mondays

This is the normal way to say that geography is one of your classes.
You can say estudio geografía, but that usually sounds more like I study geography as an academic subject, not specifically I have geography class on a certain day.

So in a school timetable context, tengo is the most natural choice.

When talking about school subjects in Spanish, it is very common to leave out the article after verbs like tener, estudiar, or gustar, especially in general school-schedule contexts:

• Tengo geografía
• Estudio química
• Me gusta la geografía / Me gusta geografía depending on context, though la is often used with gustar

In this sentence, geografía and química are treated as subject names, so no article is needed.

In Spanish, the definite article is often used with days of the week to mean on Mondays, every Monday, on Wednesdays, every Wednesday.

So:

• los lunes = on Mondays / every Monday
• los miércoles = on Wednesdays / every Wednesday

If you say just el lunes, that usually means on Monday (one specific Monday).

So here:

• Tengo geografía los lunes = I have geography every Monday
• Tengo geografía el lunes = I have geography this Monday / on Monday

In Spanish, expressions of time often appear without a preposition where English might use one.

So Este semestre naturally means:

• This semester

You do not need en here.
Spanish often does this with time expressions:

• Este año = this year
• Esta semana = this week
• Este verano = this summer

Adding en is usually unnecessary in this kind of sentence.

Because semestre is a masculine noun.

• el semestre
• este semestre

Demonstratives must agree with the noun they describe:

• este semestre because semestre is masculine singular
• esta semana because semana is feminine singular

So the form depends on the gender of the noun.

In Spanish, days of the week are normally written with lowercase letters, unlike in English.

So:

• lunes
• miércoles
• jueves

The same is usually true for months and languages:

• enero
• español

So los lunes y los miércoles is correct, not capitalized unless it starts a sentence.

They have written accents because Spanish spelling rules require them.

A quick breakdown:

• geografía: the stress falls on -fí-, so the accent shows the correct pronunciation
• química: the stress falls on quí-
• miércoles: the stress falls on miér-

These accents are part of the correct spelling and should always be written.

They are not optional, even if the meaning is still understandable without them.

Because Spanish often avoids repeating a verb when it is understood from the first part of the sentence.

So:

Este semestre tengo geografía los lunes y química los miércoles

really means:

Este semestre tengo geografía los lunes y tengo química los miércoles

The second tengo is omitted because it would be repetitive and unnecessary.

This works in English too:

• I have geography on Mondays and chemistry on Wednesdays

We do not need to repeat I have either.

Yes, that would also be grammatical.

Spanish word order is often more flexible than English.
Both of these work:

• Este semestre tengo geografía los lunes y química los miércoles
• Tengo geografía los lunes y química los miércoles este semestre

Starting with Este semestre puts a little more focus on the time frame: this semester.

So the original sentence sounds very natural and helps set the context immediately.

Normally, los lunes means every Monday as a regular habit or schedule.

So in this sentence it means the speaker’s recurring timetable:

• geography every Monday
• chemistry every Wednesday

If you wanted to talk about one specific Monday, you would normally use el lunes.

Yes. In this sentence, they clearly refer to school classes/subjects.

Because the sentence is about a timetable:

• Este semestre
• tengo
• los lunes
• los miércoles

the meaning is clearly I have geography class and I have chemistry class, not just the general disciplines.

That is a very common use of subject names in Spanish.

Y means and.

In most cases, Spanish uses y to join words or phrases:

• geografía y química

However, y changes to e before words beginning with an i sound:

• padres e hijos
• español e inglés

But here the next word is química, which does not begin with an i sound, so y is correct.

Yes, it sounds completely natural in Spain.

A speaker in Spain would very naturally say:

• Tengo matemáticas los martes
• Tengo geografía los lunes
• Tengo química los miércoles

Using tener for school subjects and los + day for recurring days is standard and natural in Spain. It would also be understood elsewhere in the Spanish-speaking world, though some regions may prefer slightly different wording in everyday speech.