Iyi günler, I am trying to disentangle the expression 

"tanıştığımıza  memnun oldum" 

So far I understood memnun is pleased (adjective)

Then oldum is from the verb olmek so it would be I have been, or I was.

But even though I think the root of tanıştığımıza is the verb to meet tanışmak, I am unable to understand the addition tığımıza. 

Can anyone please help me on this? Thanks!

ok. lets disentangle it ; 

 first part : "tanış [ the root of the verb "to meet" ] + ["dık" works like the conguction "that" , note that the letter "k" changes into "ğ"] + ımız [ personal pronoun for "us","we", its like kalem +imiz =our pencil] + a [ ending for the verb " memnun olmak" ]

so lets write this part down ---> that we met, or that our meeting,

second part ;

memnun olmak =[ to be pleased]

memnun ol [ the root of the verb] + du [ past tense] + m [ personal ending for "I" ]

So lets put them all together;

literally " I was pleased that we met "

          " I was pleased that we us met "

in other words " I am pleased to meet you "

 Other examples about "dık,duk,dük,dik"

Aldığın araba = the car that you bought

Al [to buy,to take ]+ dık [that, "k" changes into "d" ] + ın [ you ]  +  araba [ car ]

*** it doesnt necessarly has to be in past tense, it can be present tense, continues tense ,can or could]

Türkçe sevdiğim bir dildir ---> Turkish is a language that I love.

sev + dik + im

Şu an su içtiğin bardak benim --->  The glass that you are currently drinking water from is mine.

iç + dik [that,, "k" changes into "ğ"] + in [person for "you" ]

Gözünle görebildiğin her yer bana ait --> Everywhere that you could see with your eyes belongs to me.

gör [the root of verb "to see" ] + ebil [ can,could] +dik [ "that] , note that "k" changes into "ğ"] + in [person "you"]

hope it helps.. 

Thanks a lot, really good explanation.