First of all, it is certainly true that when a verb follows the preposition to, nine times out of ten, it is followed by an infinitive verb.*
- I intend to see you next week.
- I hope to see you next week.
- I would like to see you next week.
However, in the phrase I'm looking forward to seeing you next week, the to does not – technically speaking – denote an infinitive, but is a preposition in itself. And what the grammar books will also tell you is that an proposition needs to be followed by a gerund (the -ing form). You can see this in sentences like:
- We’re thinking of buying a new car.
- They’re interested in expanding their operations in Germany.
- Look forward to also belongs in this list: I look forward to seeing you this week.
There are a couple of other common constructions with to where the to is a preposition (and is therefore followed by an -ing form):
- My legs are tired. I'm not used to walking so much.
- There isn't much food in the fridge. I’ve haven’t got round to going to the supermarket yet.
- She objected to working unpaid overtime.
* Incidentally, this to which often gets affixed to the infinitive verb in English is a rather interesting phenomenon. When verbs are cited in the infinitive in English, this is frequently done with the to attached, almost as if the to were an integral part of the infinitive itself. In fact, this is exactly how it is often thought of, and an infinitive without to is known as a bare infinitive – the poor relation of the full infinitive with to! Other Germanic languages also use an equivalent preposition marker before an infinitive verb in some constructions (e.g. Dutch te, German zu, Swedish att), but English is the only language where the to has become attached to the infinitive to this extent. So much so that to 'split an infinitive' (i.e. to insert a word between the to and the following verb) is considered beyond the pale by some grammatical purists. The phrase ‘to boldly go where no man has gone before’ demonstrates, however, that in modern usage, people have been splitting infinitives for decades.