Parasyte: The Maxim at the start of Anime i.e Episode 1, the story begins showing the old couple. As the couple looks at each other the male suddenly shapes shift specifically his head change into many eyes and limbs. And sharp things came out of it and the female was shocked just looking at it. This strange thing which we just all see shocked everyone as it eats the female head in one swoop.
Parasyte: The Maxim Protagonist
The next scene shows the protagonist the anime Shinichi Izumi. As he was sleeping he heard some strange voices. Now as he awake from sleep sees some strange insect trying to enter his body. Firstly through ears but not possible due to headphones, then through the nose but he sneezes at the right time But late for him, the parasyte has already entered his body through his hand. The Parasyte tried to move his hand toward the head. He, fortunately, was listening to music through his pods so he squeezes his hand through earphones. That blocked the parasyte path and he stopped in his hand. That scene though it is in starting is the most basic thing for the story to develop and move smoothly. That thing if might have traveled to his brain he will be like male we see just as Anime began. We will get answers to all Mysteries as the story flows.
Here is the trailer of anime with its smooth animation.
Parasyte: The Maxim Begins
The story begins as Shinichi whose right hand is now numb and different somehow. While moving back from school he noticed a girl crossing the road to get her ball but a car comes and as he was going to hit the girl. Shinichi rushes and stops the car with his right hand out of instinct. But little he believed he can do it but as he sees the car it was crushed and his right hand and eye on it. He went to his room and try to stab his own hand but before he can do anything. His hand is converted into mouth and two eyes and it was speaking something which he cannot understand. The next morning he saw the same creature but divided it into half reading books. Shinichi talked to him and he was talking back so good.
Mysterious Creature What is It?
The creature which is actually a parasyte tells him his main motive was the brain. But he can’t accomplish that and he can’t now because he is fully developed in his hand now. Then the creature searched the internet and told him nothing about me is known. The protagonist thinks he must contact the police or the hospital so he can get rid of him. The parasyte proposes it is bad for him as he will lose his right hand. At the same time, I will be killed. So as I sleep you can use your right hand normally and I will live also. So begins the parasyte story and that’s how parasyte works. Then creature senses his own kind while going to school. He pursues Shinichi to follow toward his own kind. They see a dog who is eating another dog.

Migi | Parasyte
The first fight of anime begins as his hand told him to run. The dog whose brain is taken by parasyte shapeshift and follows them by flying. His hand knows dog murderous intent. Shinichi who is an average person doesn’t know how to fight his hand elongates and shapeshift and fight with an affected dog. Searching for his weak point. Finally pierces the heart and removes the heart of the dog and wins the fight. The next day Shinichi says you must have named as I have to speak to you. Then parasyre suggest Migi yet he is the fond of naming idea. Migi says it was good that he researched and was able to defeat that thing.
Parasyte: A message
Yuko discusses with Shinichi how worldwide there are deaths that are not normal. As victim’s bodies flesh is eaten and in bad shape and in mincements. Shinichi discusses with Migi what should they do as there are many like you in the world. Should we keep quiet? Migi doesn’t understand. Shinichi says as many humans are dying this is bad. Migi says you are feeling bad because this time you are being eaten It is the same as you eat most other life being for survival. What is wrong here? And demons are human actually as they eat many life forms while others which you call demons or eat one or two so they practically fit the definition. There is so much to the story as it conveys the message so accurately with its animation and storyline

“Maybe Humans are closest things to Demons alive”
— Shinichi Izumi