C. Are you interested in working for us?
a. I'm not very good at learning languages.
b. Sue must be fed up with studying.
c. What are the advantages of having a car?
d. Thanks very much for inviting me to your party.
e. How about meeting for lunch tomorrow?
f. Why don't you go out instead of sitting at home all the time?
g. Carol went to work in spite of feeling ill.
h. can also say 'instead of somebody doing something', 'fed up with people doing something'. (e.g. I'm fed up with people telling me what to do.)

C1. Before '-ing' after '-ing' (e.g. Before going out, I phoned Sarah. (not Before to go out) What did you do after leaving school?), can also say 'before I went out ~' and '~ after you left school.'
a. by '-ing' (to say how something happens) (e.g. The burglars got into the house by breaking a window and climbing in.), without '-ing'. (e.g. We ran ten kilometres without stopping.)

C2. to '-ing' (e.g. look forward to doing something etc.), to is often part of the infinitive. (to do/ to see etc.) (e.g. We decided to go out.) But to is also a preposition (like in/ for/ about / from etc.) (e.g. We drove from London to Edinburgh.)
a. If a preposition is followed by a verb, the verb ends in '-ing': in doing, about meeting, without stopping, etc. So, when to is a preposition and it is followed by a verb, we must say '-ing'. (e.g. I prefer driving to travelling by train. (not to travel))

more about the Gerund (-ing) and to ~ (infinitive)

C3. Many verbs have the structure verb + preposition (in/ for / about etc.) + object (e.g. We talked about the problem.) If the object is another verb, it ends in '-ing' (e.g. We talked about going to America)
a. succeed (in): Have you succeed in finding a job yet?
b. insist (on): They insisted on paying for the meal.
c. think (of): I'm thinking of buying a house.
d. dream (of): I wouldn't dream of asking them for money.
e. approve (of): He doesn't approve of swearing.
f. decide (against): We have decided against moving to London.
g. feel (like): Do you feel like going out tonight?
h. look forward (to): I'm looking forward to meeting her.
i. can also say 'approve of somebody doing something', 'look forward to somebody doing something'. (e.g. I don't approve of people killing animals for fun.

more about the Gerund (-ing) and to ~ (infinitive)

C4. Verb + object + preposition + '-ing'
a. congratulate (on): I congratulated Liz on getting a new job.
b. accuse (of): They accused us of telling lies.
c. suspect (of): Nobody suspected the general of being a spy.
d. prevent (from): What prevented you from coming to see us?
e. stop (from): The rain didn't stop us from enjoying our holiday.
f. thank (for): I forgot to thank them for helping me.
g. excuse (for): Excuse me for being so late.
h. forgive (for): Please forgive me for not writing to you.
i. can say 'stop somebody doing' or 'stop somebody from doing' (e.g. You can't stop me doing what I want. or You can't stop me from doing what I want.
j. Some of these verbs are often used in the passive. (e.g. We were accused of telling lies.)
k. Note that we say 'apologise to somebody for ~'. (e.g. I apologised to them for keeping them waiting. (not I apologised them))

more about the Gerund (-ing) and to ~ (infinitive)