alıp comes from the verb almak = to take

The ´ip´ suffix is used in Turkish as a way of shortening sentences, where both the verbs have the same subject and personal suffix.

So to get the meaning of alıp in your sentence, you have to look at the last verb olacağım (I will be) and therefore here

alıp = alacağım ve ... (I will take and ....)

I will take massage lessons and .......

This is how tunci explains the -ip thing in an old thread. Use the search and you will probably find this issue in many places.

-ip is very close to ´and´. You save the effort of using the inflectional suffixes twice.

In your example

                     " masaj dersleri alıp bitirmiş olacağım"

it is like almış ve bitirmiş.

My Try for the meaning:

                     ´I will have (taken and) completed the massage lessons.´

Interesting, Henry. You connected alıp to olacağım, I connected it to bitirmiş. This is what happens when two learners unite the drops of their wisdom.

Someone help.

You are both wrong. You should connect it to "bitirmiş olacağım"

,

Can I get some clarification please 

So -i bitirmiş olmak is a compound verb meaning to be through with, to be completed, tamamlamak gibi mi?

bitirmiş olacağım = I will have completed

and now my translation becomes .......

I will have taken and completed the massage lessons. Doğru mu?

And this is also exactly how Abla translated it. 

Your last translation is correct. I just made a joke because abla said you two had connected "alıp" to different members of the compound verb "bitirmiş olmak". I just mentioned you should have connected it to the whole verb. Of course this joke only makes sense in Turkish

Note: By the way I think "bitirmiş" is noun in the compund verb. What do you say?

It depends on how you want to see the object (masaj dersleri). If it is governed by bitirmiş olacağım then you can see bitirmiş as a noun (or adjective) in that compound verb which as a wholeness takes accusative object. But if masaj dersleri is the object of bitirmiş then of course it it still a verb  -  nouns do not take objects. No idea really which interpretation is closer to the truth.

Great explanation. But don´t forget some nouns can take objects in Turkish. For example "bitirmiş" is an adjective verb. It can function as a noun but it can still take object.

Another example:

Okumayı bilen adam.

"bilen" is an adjective verb here. And okumayı is the object.

I think there are adjective verbs in English too. For example:

ongoing process

You see ongoing is an adjective but it is also a verb.

I have a question here. Can adjective verbs take objects in English? I guess they can´t because of structural differences. What is your opinion?

Participles and infinitives are neither pure verbs nor pure adjectives/nouns. They have features of both.

I cannot think about an example where an English verb functions as an adjective and takes and object. And I wonder if the reason could be put into words. I found a nice page about it but with no such examples:

                    http://www.langust.ru/unit_co/unit023c.shtml

Maybe our native English speakers can clarify it. Or si++. He wrote about these things in the "Gerunds" thread.

Thank you everyone, this was helpful. Herkese çok teşekkürler