Learn Hardcore German: Die Lehrerin erklärt, die Wahrheit sei wichtig, und der Satzbau dieses Gedichts sei nicht schwer. - The teacher explains that the truth is important and that the sentence structure of this poem is not difficult.

Sei is the subjunctive I (Konjunktiv I) form of sein. It is used here for reported (indirect) speech after the reporting verb erklärt.

Direct speech:

Die Lehrerin erklärt: „Die Wahrheit ist wichtig, und der Satzbau dieses Gedichts ist nicht schwer.“

Indirect speech (reported):

Die Lehrerin erklärt, die Wahrheit sei wichtig, und der Satzbau dieses Gedichts sei nicht schwer.

Using sei instead of ist shows that the speaker is reporting what the teacher explains, not stating it as their own assertion. In everyday spoken German, many people would simply say:

Die Lehrerin erklärt, dass die Wahrheit wichtig ist und der Satzbau dieses Gedichts nicht schwer ist.

That version uses the indicative (ist) and is stylistically more neutral/colloquial. The version with sei sounds more formal and “written,” like in newspapers or academic texts.

What exactly is sei grammatically, and what are the other forms?

Sei is the 3rd person singular Konjunktiv I of sein (to be).

Konjunktiv I of sein:

ich sei
du seiest
er / sie / es sei
wir seien
ihr seiet
sie / Sie seien

In your sentence, the subjects are die Wahrheit and der Satzbau dieses Gedichts, both 3rd person singular, so the correct Konjunktiv I form is sei.

Why is there no dass after erklärt? Could we say Die Lehrerin erklärt, dass …?

Yes, you can say it with dass, and that is very common:

Die Lehrerin erklärt, dass die Wahrheit wichtig sei und dass der Satzbau dieses Gedichts nicht schwer sei.
In everyday speech: … dass die Wahrheit wichtig ist und dass der Satzbau dieses Gedichts nicht schwer ist.

In your sentence, dass is simply omitted, which is allowed after verbs of saying/thinking like sagen, erklären, meinen, glauben. When dass is omitted, the clause that follows has main-clause word order (verb in second position):

with dass: …, dass die Wahrheit wichtig sei. (verb at the end)
without dass: …, die Wahrheit sei wichtig. (verb in 2nd position)

So the version without dass is a somewhat more compact, slightly formal or literary way of expressing indirect speech.

Is the word order die Wahrheit sei wichtig normal? Why isn’t sei at the end?

Yes, it is normal because there is no subordinating conjunction like dass.

With dass (subordinate clause):
…, dass die Wahrheit wichtig sei.
→ Verb (sei) goes to the end.
Without dass (content clause after a comma):
…, die Wahrheit sei wichtig.
→ Verb (sei) is in second position, like in a main clause.

So the comma plus Konjunktiv I here introduces a reported-content clause that behaves in word order like a main clause.

What case is dieses Gedichts, and how do we know?

Dieses Gedichts is genitive singular.

The base noun is das Gedicht (neuter).
Genitive singular of das Gedicht is des Gedichts.
With the demonstrative dies-, you get:
dieses Gedichts = of this poem.

It depends on der Satzbau:

der Satzbau dieses Gedichts
literally: the sentence structure of this poem.

So dieses Gedichts is a genitive complement of Satzbau.

Could we say der Satzbau von diesem Gedicht instead of der Satzbau dieses Gedichts?

Yes, grammatically you can say:

der Satzbau von diesem Gedicht

However:

Genitive (der Satzbau dieses Gedichts) sounds more formal and more typical of written German.
von + Dativ (der Satzbau von diesem Gedicht) sounds more colloquial and slightly heavier stylistically.

Both are understandable. In careful written language, the genitive version is usually preferred.

Why is it der Satzbau and not den Satzbau?

Der Satzbau here is nominative singular masculine, functioning as the subject of the clause:

der Satzbau dieses Gedichts → subject
sei → verb (3rd person singular)
nicht schwer → predicate adjective

The pattern is:

Der Satzbau dieses Gedichts sei nicht schwer.
The sentence structure of this poem is (is said to be) not difficult.

If Satzbau were an object, you might see den Satzbau, but here it clearly acts as the subject of the second reported clause.

Why is there a comma before und in …, die Wahrheit sei wichtig, und der Satzbau …? Is it required?

The comma before und separates two reported content clauses that belong to erklärt:

die Wahrheit sei wichtig
(und) der Satzbau dieses Gedichts sei nicht schwer

So the structure is:
Die Lehrerin erklärt, [1], und [2].

According to modern punctuation rules, when two subordinate (or content) clauses of the same type are linked by und, the comma can be optional. So both of these are acceptable:

Die Lehrerin erklärt, die Wahrheit sei wichtig und der Satzbau dieses Gedichts sei nicht schwer.
Die Lehrerin erklärt, die Wahrheit sei wichtig, und der Satzbau dieses Gedichts sei nicht schwer.

The version with the comma can feel a bit clearer because it visually separates the two pieces of information.

Does nicht schwer mean the same as leicht? Why use a negation instead of a positive adjective?

Nicht schwer literally means “not difficult”, while leicht means “easy”.

In practice:

nicht schwer is a bit more neutral and modest:
It’s not hard (don’t worry about it too much).
leicht is more positively:
It’s easy.

Both are correct here. The choice is about tone:

Der Satzbau dieses Gedichts sei nicht schwer.
→ Emphasizes that it’s not a problem / not too hard.
Der Satzbau dieses Gedichts sei leicht.
→ Emphasizes that it’s actually easy.

Teachers often use nicht schwer because it sounds slightly less absolute and more encouraging.

How would the sentence look in direct speech, and what is the difference in meaning or style?

Direct speech version:

Die Lehrerin erklärt: „Die Wahrheit ist wichtig, und der Satzbau dieses Gedichts ist nicht schwer.“

Difference:

Direct speech uses the teacher’s exact words (ist), indicated by quotation marks or a colon. The narrator takes over her voice.
Indirect speech (your original sentence) uses Konjunktiv I (sei) to show that this is a report of what she says, not necessarily quoted word for word.

Stylistically:

Direct speech feels more vivid and immediate.
Indirect speech with sei feels more formal, distant, or report-like, and is common in news reports and academic writing.

Can we change erklärt to the past tense, and what happens to sei?

Yes, you can put erklärt into the past (erklärte) without changing sei:

Die Lehrerin erklärte, die Wahrheit sei wichtig, und der Satzbau dieses Gedichts sei nicht schwer.

In indirect speech with Konjunktiv I, the subjunctive form (sei) does not normally change with the tense of the reporting verb. It stays sei even though erklärte is past.

If you drop Konjunktiv and use the indicative (more colloquial), you would usually shift tenses:

Die Lehrerin erklärte, dass die Wahrheit wichtig war und der Satzbau dieses Gedichts nicht schwer war.

So:

Konjunktiv I: tense of the reported clause is largely independent and often stays in the present (sei) to show it’s a general statement.
Indicative: more likely to follow sequence of tenses with the reporting verb.