One of the main takeaways from this dialogue is Plato's theory of the ideal state. He presents a vision of an ideal society governed by philosopher-kings, individuals possessing wisdom, knowledge, and understanding of the ideal forms. Plato argues that the best society is one where people are assigned to occupations based on their natural abilities, with a strict division of labor and a hierarchical structure of rulers, soldiers, and producers. 

Another significant concept in the "Republic" is Plato's allegory of the cave. He emphasizes the importance of education and philosophical enlightenment to liberate individuals from the shadows of the cave and lead them to perceive the true reality of the forms. Plato's theory of forms, which details the existence of a realm of perfect and unchanging forms beyond the imperfect and changing physical world, is another crucial aspect of the dialogue. 

Overall, the "Republic" addresses various themes such as political philosophy, ethics, metaphysics, epistemology, and the nature of justice, making it a foundational text in philosophical discussions about the ideal state, the pursuit of knowledge, and human society.