The exact answer has not been revealed, but some conclusion can be drawn from different episodes and chapters of anime and manga.

The prelude of several episodes of Attack on Titan stated that:

Over a hundred years ago, humanity suddenly found itself faced with a new predator. They were more powerful than humans. Humanity was immediately pushed to the brink of extinction. The survivors built three walls: Maria, Rose, and Sina.

From the anime and manga:

• The Female Titan spared Armin's life several times.
• The walls were built with the exoskeletons of titans.
• Colossal Titan, Armored Titan, Female Titan (i.e. Bertolt Hoover, Reiner Braun, Annie Leonhart respectively) and other Titan Shifters actually lived among humans.
• Ymir turned into titan and protected her friends from other titans.
• Rich people and the top brass who mainly lived inside Wall Sina knew a lot about the titans, the walls and the titan inside the walls.
• The titans who broke through the wall and led other titans inside were mainly the Colossal Titan and Armored Titan, and their objective was to search for the mysterious power known as the "Coordinate".

These points lead me to conclude that their main intention is not to destroy humanity, but to find the Coordinate ability for which they may destroy humanity. The relation of the Titan Shifters with human, and their willingness to sacrifice their lives for their friends shows that their main intention was not to destroy humanity. And humans are not as weak as they seem to be; titans need to make some effort to destroy all humans, and those titans with brain know that.

The exact answer has not been revealed, but some conclusion can be drawn from different episodes and chapters of anime and manga.

The prelude of several episodes of Attack on Titan stated that:

Over a hundred years ago, humanity suddenly found itself faced with a new predator. They were more powerful than humans. Humanity was immediately pushed to the brink of extinction. The survivors built three walls: Maria, Rose, and Sina.

From the anime and manga:

• The Female Titan spared Armin's life several times.
• The walls were built with the exoskeletons of titans.
• Colossal Titan, Armored Titan, Female Titan (i.e. Bertolt Hoover, Reiner Braun, Annie Leonhart respectively) and other Titan Shifters actually lived among humans.
• Ymir turned into titan and protected her friends from other titans.
• Rich people and the top brass who mainly lived inside Wall Sina knew a lot about the titans, the walls and the titan inside the walls.
• The titans who broke through the wall and led other titans inside were mainly the Colossal Titan and Armored Titan, and their objective was to search for the mysterious power known as the "Coordinate".

These points lead me to conclude that their main intention is not to destroy humanity, but to find the Coordinate ability for which they may destroy humanity. The relation of the Titan Shifters with human, and their willingness to sacrifice their lives for their friends shows that their main intention was not to destroy humanity. And humans are not as weak as they seem to be; titans need to make some effort to destroy all humans, and those titans with brain know that.

The exact answer has not been reveled but some conclusion can be drawn form the different episode and chapter of anime and manga.

From few episode OP of Attack on Titan, it is stated that:

Over a hundred years ago, humanity suddenly found itself faced with a new predator. They were more powerful than humans. Humanity was immediately pushed to the brink of extinction. The survivors built three walls: Maria, Rose, and Sina.

• Female titan spared Armin's life few times

The walls are built with the exoskeletons of titans.

Colossal, Armored, Female titan Bertolt Hoover, Reiner Braun, Annie Leonhart and other titan that can shift their titan form live with human

Yamir turn into the titan and protect her friends from other titan

Renowned, Rich and higher level people who mainly live inside Sina wall knows a lot about titan, wall and titan living with wall.

Titan who break the wall and lead other titan inside are mainly Colossal and Armored titan and their objective was to search mysterious power known as the "Coordinate".

These point lead that their main intention is not to destroy humanity but to find Coordinate for which they may destroy Humanity. Relation of Titan shifter with human and scarifying their live for their friends shows their main intention was not to destroy humanity. And human are not as weak as they seem to be, titan need to make some effort to destroy all humans and those Titan with brain know that.

The exact answer has not been revealed, but some conclusion can be drawn from different episodes and chapters of anime and manga.

The prelude of several episodes of Attack on Titan stated that:

Over a hundred years ago, humanity suddenly found itself faced with a new predator. They were more powerful than humans. Humanity was immediately pushed to the brink of extinction. The survivors built three walls: Maria, Rose, and Sina.

From the anime and manga:

• The Female Titan spared Armin's life several times.
• The walls were built with the exoskeletons of titans.
• Colossal Titan, Armored Titan, Female Titan (i.e. Bertolt Hoover, Reiner Braun, Annie Leonhart respectively) and other Titan Shifters actually lived among humans.
• Ymir turned into titan and protected her friends from other titans.
• Rich people and the top brass who mainly lived inside Wall Sina knew a lot about the titans, the walls and the titan inside the walls.
• The titans who broke through the wall and led other titans inside were mainly the Colossal Titan and Armored Titan, and their objective was to search for the mysterious power known as the "Coordinate".

These points lead me to conclude that their main intention is not to destroy humanity, but to find the Coordinate ability for which they may destroy humanity. The relation of the Titan Shifters with human, and their willingness to sacrifice their lives for their friends shows that their main intention was not to destroy humanity. And humans are not as weak as they seem to be; titans need to make some effort to destroy all humans, and those titans with brain know that.