He asked me whether I didn’t want to go there. 
I replied that I would book tickets.

rules: tenses of direct quote are moved one step into the past for indirect version, further changes to guarantee accuracy may be needed (e.g. today, this, pronouns); reporting verb "tell" always with addressee
questions: no auxiliaries, use whether or if for non-"wh" questions

Iceland is believed to have existed for millions of years.

In 1960, Iceland was thought to be boring.

Last year, northern lights were rumoured to have been seen.

time of reporting: indicated in passive tense of reporting verb
time of reported event: if = reporting time --> "to + inf."
if earlier than reporting time --> "to have been + past part."

People who have seen them will never forget them.

defining: necessary for sentence to make sense, no commas
non-defining: additional information, commas, no "that" as relative pronoun

experiences. 

Having been to Iceland twice, my best friend loves it.
rule: subjects in both clauses must be identical!
use: participle clauses can provide time, reason, result, contrast or condition to the main clause

before ‘that’ 

after an if-clause 
after linking words at beginning of sentence
after participle and adverbial clauses 

The university I go to is in the UK.

American universities are more expensive than Swiss universities.

indefinite article (a/an): first time you mention sth, unspecific
definite article (the): when it's clear what/who is meant, plus specific rules (cf. grammar overview)
no article: general statements

 

Eine europäische Universität ist eine attraktive Option.
An european university is a attractive option.
--> An European university is an attractive option.