Learn Hardcore Greek: Σήμερα την βλέπω μόνο στο πανεπιστήμιο.

It stands for a female person (or a feminine noun) that is already known from the context.
If you wanted to stress it more strongly (for example, to contrast her with someone else), you could use the stressed form αυτήν:

Σήμερα αυτήν βλέπω μόνο στο πανεπιστήμιο.
Today it’s her (as opposed to someone else) that I see only at the university.

In neutral speech, the unstressed την is the normal choice.

Why does την come before βλέπω instead of after it, like in English?

In Modern Greek, weak object pronouns (like την, τον, το) normally go before the verb when the verb is a normal finite verb in a main clause.

So:

Την βλέπω. = I see her.
(not ❌ Βλέπω την with the weak pronoun)

They typically go after the verb only in specific structures, for example:

After the imperative: Δες την. (See her.)
After να (subjunctive): να τη δεις (to see her / that you see her)
After θα (future): θα τη δω (I will see her)
After μη(ν) (negative imperative/subjunctive): μην τη δεις (don’t see her)

So Σήμερα την βλέπω μόνο στο πανεπιστήμιο follows the normal Greek word order for a weak object pronoun.

Do I need to say εγώ for “I”? Could I say Εγώ σήμερα την βλέπω μόνο στο πανεπιστήμιο?

You don’t need εγώ; the verb ending in βλέπω already shows that the subject is I.

Σήμερα την βλέπω μόνο στο πανεπιστήμιο.
is the neutral way: Today I only see her at the university.

You add εγώ when you want to emphasize that it is me (as opposed to someone else):

Εγώ σήμερα την βλέπω μόνο στο πανεπιστήμιο.
I (not somebody else) see her only at the university today.
Σήμερα την βλέπω μόνο στο πανεπιστήμιο εγώ.
Also possible, with emphasis on εγώ at the end.

So:

Without εγώ = neutral.
With εγώ = contrastive / emphatic “I”.

What is στο exactly? Is it one word or a combination?

Στο is a contraction of two words:

σε (preposition: in, at, to)
το (neuter singular definite article: the)

σε + το → στο

So:

στο πανεπιστήμιο = in/at the university

This contraction is standard and almost always used in both speech and writing. Similar contractions:

σε + τον → στον (e.g. στον δρόμο – in the street)
σε + την → στην (e.g. στην πόλη – in the city)
σε + τα → στα (e.g. στα πανεπιστήμια – at the universities)

Why is πανεπιστήμιο in that form? Why not something like πανεπιστήμιον, or the article written separately?

A few points together:

Form of the noun
Πανεπιστήμιο is the Modern Greek form of the noun “university.”
- It is neuter, singular, and here it is in the accusative case (after the preposition σε).
- For neuter nouns, nominative and accusative singular look the same: πανεπιστήμιο.
The form πανεπιστήμιον is older / Katharevousa or Ancient Greek style, not used in normal Modern Greek.
Case choice
After σε, Modern Greek normally uses the accusative:
- σε (το) πανεπιστήμιο → στο πανεπιστήμιο
Where is the article?
The article το is still there, but it has fused with σε to form στο, as explained above.
If you “uncontract” it, the structure is:
- σε το πανεπιστήμιο → στο πανεπιστήμιο

So στο πανεπιστήμιο is fully regular Modern Greek: preposition + definite article (contracted) + neuter noun in the accusative.

What does μόνο do here, and can I move it to other positions?

Μόνο is an adverb meaning only. In this sentence it is placed before στο πανεπιστήμιο, so its natural scope is the place:

Σήμερα την βλέπω μόνο στο πανεπιστήμιο.
Today I see her only at the university (not anywhere else).

You can move μόνο, but its position changes what exactly is “only”:

Σήμερα μόνο την βλέπω στο πανεπιστήμιο.
Today I only see her at the university
→ Emphasis that the only thing you do with her is see her (you don’t talk, you don’t study together, etc.).
Μόνο σήμερα την βλέπω στο πανεπιστήμιο.
Only today do I see her at the university
→ Emphasis that today is the only day this happens.
Σήμερα την βλέπω στο πανεπιστήμιο μόνο.
Less natural; it sounds like μόνο is tagged on at the end. Not wrong, but the earlier versions are clearer.

So yes, you can move μόνο, but you must be aware that you are changing the focus of “only” each time.

Can I move σήμερα to another place in the sentence? Does the meaning really change?

Yes, σήμερα can move quite freely, because Greek word order is relatively flexible. All of these are grammatical:

Σήμερα την βλέπω μόνο στο πανεπιστήμιο.
Την βλέπω σήμερα μόνο στο πανεπιστήμιο.
Την βλέπω μόνο στο πανεπιστήμιο σήμερα.
Μόνο στο πανεπιστήμιο σήμερα την βλέπω.

If you say them without special emphasis, the basic meaning stays the same:
Today I only see her at the university.

However, placement can be used for emphasis:

Putting σήμερα at the very beginning often gives a bit more weight to “today”.
Putting it just before the part you want to highlight can make that contrast clearer in spoken Greek.

For everyday purposes, you can treat these as minor nuance differences; the core meaning does not fundamentally change.

What tense/aspect is βλέπω, and how would the meaning change with είδα or θα τη δω?

Βλέπω is present indicative, imperfective aspect. In this sentence, with σήμερα, it can mean:

A regular, present-time situation:
Today I (habitually/usually) see her at the university.
Or a near-future arrangement in colloquial speech:
Today I’m seeing her at the university.

Compare:

Σήμερα την είδα μόνο στο πανεπιστήμιο.
- είδα = aorist (simple past)
- Meaning: Today I only saw her at the university.
  → One completed event in the past (earlier today).
Σήμερα θα τη δω μόνο στο πανεπιστήμιο.
- θα δω = aorist future
- Meaning: Today I will only see her at the university (not anywhere else).
  → One expected future event.
Σήμερα θα τη βλέπω μόνο στο πανεπιστήμιο.
- θα βλέπω = future, imperfective
- Meaning: Today I’ll be seeing her only at the university (repeatedly / for a period of time).

So:

βλέπω = present, ongoing/general.
είδα = one completed past event.
θα τη δω = one (or a few) future events.
θα τη βλέπω = ongoing or repeated seeing in the future.

Why is την sometimes written τη? Which one is correct in this sentence?

The pronoun has a form with -ν (την) and a form without it (τη). Traditional spelling rules say:

Keep the final -ν of την / τον:
- before a vowel
- before the consonants κ, π, τ, ξ, ψ, γκ, μπ, ντ, τσ, τζ
You may drop it before other consonants.

Since βλέπω starts with β, which is not in that list, the traditional rule would give:

τη βλέπω

However:

In real modern usage, many speakers keep -ν almost always: την βλέπω.
Both τη βλέπω and την βλέπω are commonly seen in writing today.

So, in practice:

τη βλέπω = more strictly following the traditional rule.
την βλέπω = very common, fully understood, often preferred in informal writing.

You can safely use either; just be consistent in a given text.

How would the sentence change if I were talking about a man instead of a woman?

You only need to change the object pronoun την to the masculine form τον:

Σήμερα τον βλέπω μόνο στο πανεπιστήμιο.
Today I only see him at the university.

For a neuter (an object, a thing), you would use το:

Σήμερα το βλέπω μόνο στο πανεπιστήμιο.
Today I only see it at the university.
(for a neuter noun, e.g. το ρομπότ, το αυτοκίνητο etc.)

Can την also mean “it” in this sentence? How would I know?

Yes. Την can mean “it” when it refers to a feminine noun.

Examples of feminine nouns:

η τηλεόραση (the television)
η πόρτα (the door)
η μηχανή (the machine)

In such a context:

Σήμερα την βλέπω μόνο στο πανεπιστήμιο.
could mean:
- Today I only see *her at the university.*
  or
- Today I only see *it at the university.* (e.g. a particular machine that is at the university)

Greek relies on context to distinguish:

If the conversation is about a woman (e.g. Maria), it means her.
If the conversation is about a feminine object (e.g. η μηχανή), it means it.

Is βλέπω used like English “see” with direct objects? Can I use it with other objects in the same way?

Yes. Βλέπω is a transitive verb and works very similarly to English see:

Βλέπω την Μαρία. – I see Maria.
Βλέπω το σπίτι. – I see the house.
Τον βλέπω κάθε μέρα. – I see him every day.
Δεν τη βλέπω συχνά. – I don’t see her often.

You can use it with:

Noun objects: βλέπω τον φίλο μου (I see my friend)
Pronoun objects: τη βλέπω, τον βλέπω, τους βλέπω etc.

So in Σήμερα την βλέπω μόνο στο πανεπιστήμιο, βλέπω simply takes την as its direct object, exactly like see her in English.