Is it normal that i still love him?

Sooo me and this guy have been on and off in a very hectic and probably to most, unhealthy relationship for almost 4 years. Weve had alooot of good times but also alot of bad. Like all the nights we lay in the back end of his truck with all my pillows and blanket and just stare into the sky and talk the night away. I remember all the times hed surprise me with flowers and give me cards that said the cutest things. He would sing me love songs and hold me til I fell asleep. He would write me poems. I remember on valentines day he cried cuz we out and he let me pick out some clothes cuz I needed them and his card got denied. And that same valentines day i remember he hid a red box with a beautiful heart necklace for me in the fridge cuz I used to always open the fridge hoping there would be something in the fridge to eat. I remember the night before my birthday we were out walking the neighborhood and I saw this GIANT sunflower in someones yard and I just stood there admiring it. My birthday night he went and cut it down and gave it to me. I thought it was soo sweet.

I still remember the first time he got physical with me.... I woke up and didnt felt good so I stayed in bed. He came over yelling at me to get the fuck outta bed and all this. So I finally got outta bed and yelled and was like there are you fucking happy?! He shoved me against the wall and ripped the hollister dress off of me that I was wearing and was like dont you ever fucking talk to me like that again. Before I knew it we were fighting..... He was pulling me around the house by my hair threw me to the floor i had scratches all over me. It was pretty bad. He flipped the bed threw the night stand at the wall broke the alarm clock and almost broke the lamp... He even ended up stomping a hole in the wood floor. (we lived in a historic house with wood floors) All i can remember was crying and trying to get him off of me... We talked like a week or so later and things were fine. This was in 2010. Weve been back together countless times since then. Things get better and then get worse better then worse. The last fight we got into this past october of 2012 he ended up giving me a black eye idk how tho. It all just happened soo fast. I just remember him yelling at me for this and for that and so I walked away well he followed me and continued to yell at me. So i went to go lock myself in the room so he could chill out. I walked out the door and before I knew it i was on the floor trying to fight him off of me. In the process I had a goose egg above my eye, a black eye, and a scratch down my face.... Cops were called but he was no where to be found. He even ripped my shirt and bra off of me that night.... This all happened in october and to this day I was talking to him up until end of november. Well things were already sour for me where I was living, didnt have money to pay the bills so the electric got turned off. I ended up moving in with some friends... Then beginning of december I moved out of state to be with my family. I come to find out the night I get here, that he is in jail for resisiting arrest and physical force on a police officer. Havent had any contact with him for almost 3 weeks and I feel like a piece of me is missing... I dont understand whats wrong with me. Why do I still miss and love him? Why do I continue to put up with this? Why am I crying over him? It just doesnt make sense. I wasnt taught that love was abuse and name calling. i wasnt brought up around any of that. So why am i allowing this to happen to me. It just doesnt make sense.... All I want is to hear his voice and talk to him and be in his arms and just have him with me. Since Ive been here I hardly even sleep anymore. I call his phone even though i know hes in jail just to hear his voice on the answering machine.... Things arent always bad... When they are good its the best Im the happiest person alive and no matter what as long as hes with me it feels like nothing can go wrong. I dont understand after all hes put me through that Im still with him and just wanna see him. It just doesnt make sense. I hardly remember the bad. I always remember the good. So is it normal,that even though things can be really bad at times, all I want right now is to be with him and I cant cuz im 1600 miles away and hes in jail. Is it normal that even after all the abuse I still love and miss him?