'n/yn is needed to make the link between dw i, rwyt ti, etc and a verb-noun such as mynd, dod, gweld, etc:

• Dw i'n gweld y ci. - I see the dog.
• Rwyt ti'n mynd i Aber - You are going to Aber.

eisiau is not a verb-noun, and the pattern dw i eisiau, etc is an exceptional one in Welsh - the 'n/yn is not used. This is explained in the course notes.

[The reason for this is that there is a more formal form that is occasionally used where there is another word between dw i and eisiau, but that word has been dropped in colloquial use.]