Ablative absolute
The ablative absolute construction consists of:
1. a noun or pronoun
2. a modifier (adjective, appositive, participle)
Both are in the ablative case.
Rōmā vīsā, virī gaudēbant.
With Rome having been seen, the men rejoiced.
hīs rēbus audītīs, coepit timēre.
With these things having been heard, he began to fear.
From these exx. you can see that the abl. abs. phrase is only loosely connected to the main clause. It usually gives general circumstances relating to the sentence, but is itself self-contained, & separate from the sentence syntactically.
Translation
The abl. abs., since it gives general circumstances, carries often additional meaning (as participles do). It can be used in a temporal (when, while, as), causal (since, because), concessive (although), or conditional (if) sense.
Exempla
1. The composition of the abl. abs.:
eō imperium tenente [pronoun + part.], ēventum timeō
hīs rēbus audītīs [noun + part.], coepit timēre
tē duce [pronoun + appositive], nihil timēbimus
duce incertō [noun + adjective], bellum terreō
2. Senses of the abl. abs.
temporal: eō imperium tenente, ēventum timeō.
With him holding power [=while he is], I fear the outcome.
causal: duce incertō, bellum terreō.
With our leader unsure [=because he is], I'm afraid of war.
concessive: hīs rēbus audītīs, coepit timēre.
With these things having been heard [=although they were], he began to fear.
conditional: tē duce, nihil timēbimus.
With you our leader [=if you are], we'll fear nothing.
Passive periphrastic
The passive periphrastic consists of the future passive participle (also called the gerundive) plus a form of sum. The participle (being an adjective) agrees with the subject. The participle carries a sense of necessity: this is what is emphasized in the passive periphrastic.
id faciendum est.
It must be done.
liber cum cūrā legendus est.
The book has to be read with care.
Dative of agent
This construction is passive, but if the 'doer' is specified, it is not by ablative of agent, but by the dative of agent.
id faciendum est tibi.
it must be done by you.
liber mihi cum cūrā legendus est.
The book has to be read with care by you
Exempla
illa puella [subj.] omnibus [dat. of agent] laudanda est [pass. periphrastic]
That girl must be praised by everyone.
pax ducibus nostrīs petenda erat.
Peace had to be sought by our leaders.