Jeg går gennem sikkerhedskontrollen, efter at jeg har tjekket ind.

In Danish, the present tense often covers both ideas.

So jeg går can mean:

• I go
• I am going
• sometimes even I will go, if the context makes the future meaning clear

Danish does not use a separate progressive form the way English does (am going, am checking in, etc.). So the simple present does more work.

In this sentence, jeg går gennem sikkerhedskontrollen can sound like:

• a general sequence of actions
• a routine
• a planned action

Context tells you which reading is intended.

The basic form is at gå = to go / to walk.

Går is the present-tense form:

• at gå — infinitive
• går — present
• gik — past
• gået — past participle

This verb is irregular, so it is worth memorizing.

Because Danish usually writes compound nouns as one word.

Here you have:

• sikkerhed = security
• kontrol = control/check

Together:

• sikkerhedskontrol = security check / security control

And then the definite ending is added:

• sikkerhedskontrollen = the security check/control

This is very normal in Danish. English often writes these ideas as two words, but Danish commonly joins them.

Because Danish usually adds the definite article to the end of the noun instead of putting a separate word in front.

So:

• en sikkerhedskontrol = a security check
• sikkerhedskontrollen = the security check

The noun sikkerhedskontrol is a common-gender noun, so its definite singular ending is -en.

Because efter at introduces a whole clause.

Compare:

• efter check-in / efter indtjekning
  Here efter is followed by a noun phrase.

• efter at jeg har tjekket ind
  Here efter at is followed by a full clause with subject + verb.

So:

• efter = after + noun
• efter at = after + clause

That is why at is needed here.

Because the sentence presents the check-in as a completed action that happens before going through security.

har tjekket ind is the present perfect:

• har
  • past participle

It is used here much like English have checked in in a clause such as after I have checked in.

So the sequence is:

1. I check in
2. then I go through security

Danish often uses the present perfect in this kind of “first this, then that” structure.

Because tjekke ind is a verb + particle combination, similar to English check in.

Its basic form is:

• at tjekke ind

In compound tenses, the past participle stays with the auxiliary, and the particle stays separate:

• jeg har tjekket ind

Compare:

• jeg tjekker ind
• jeg tjekkede ind
• jeg har tjekket ind

So ind is not a prefix here; it is a separate particle.

Because efter at introduces a subordinate clause.

In a Danish main clause, the finite verb normally comes in second position:

• Jeg går gennem sikkerhedskontrollen.

But in a subordinate clause, the order is usually:

• subject + finite verb + other elements

So:

• efter at jeg har tjekket ind

not:

• efter at har jeg tjekket ind

That inversion (har jeg) belongs to main-clause patterns, not this kind of subordinate clause.

Because the sentence is using a comma before a subordinate clause.

In Danish, you may see two accepted comma styles:

• with start comma
• without start comma

So both of these can be correct, depending on the comma system being used:

• Jeg går gennem sikkerhedskontrollen, efter at jeg har tjekket ind.
• Jeg går gennem sikkerhedskontrollen efter at jeg har tjekket ind.

The version you were given uses the style with the comma.

Yes, often you can.

Both gennem and igennem can mean through. In many everyday contexts, they are very close in meaning.

So you may hear:

• Jeg går gennem sikkerhedskontrollen
• Jeg går igennem sikkerhedskontrollen

Very broadly:

• gennem often sounds a bit more neutral or standard
• igennem can sound a bit more spoken or can emphasize getting all the way through

But in this sentence, both are understandable and natural.