 Emergence is one of the central concepts within systems and complexity theory as it describes a universal process of becoming or creation. A process whereby novel features and properties emerge when we put elementary parts together as they interact and self-organize to create new patterns of organization. Emergence being a highly abstract concept is literally everywhere, from the evolution of the universe to the formation of traffic jams, from the development of social movements to the flocking of birds, from the cooperation of trillions of cells giving rise to the human body, to the formation of hurricanes and financial crises. Although the ideas of emergence have been of interest to many for millennia, it has often been seen as something of a mystery. But with the development of complexity theory, we increasingly have the computational and conceptual tools to understand it in a structured, scientific fashion. During the course, we will be drawing upon different ideas in complex systems theory to build up a framework for understanding emergence in a coherent fashion. More specifically, we will explore emergence as a form of nonlinear pattern formation, where synergies between elementary parts give rise to self-organization and the formation of a distinct pattern that creates new, emergent levels of organization that are driven by an evolutionary dynamic. After giving an overview of emergence theory, the course is designed around four main sections. In the first section, we start off by talking about patterns of correlation in general before going on to look at synergistic interactions that are the foundations to emergence. The next section is focused on pattern formation, the question of how the parts come to self-organize, to synchronize their states into forming a new level of organization. Here, we will talk about the two primary different types of emergence that are often used categorizations, what are called strong and weak emergence. In the third section, we will look at the idea of integrative levels, how synergies give rise to pattern formation and the emergence of new levels of organization called integrative levels. We will talk about how these different levels come to have their own irreducible internal structure and processes that result in a complex dynamic between the micro and macro levels of organization. In the last section of the course, we will look at how emergence plays out over time within some process. We will talk about the edge of chaos hypothesis, how self-organizing emergent systems never quite lock into place but instead evolve through a dynamic interplay between order and disorder to create novel phenomena at new levels of complexity. This is an introductory course and is non-technical. However, it is important to note that the concept of emergence is highly abstract. To do it justice, we will have to use high-level abstractions. As such, students will need to feel comfortable with formal abstract models. The course should be accessible without need for any specific background in science and should be of relevance to many different domains, in particular for those in the areas of computer science, biology and ecology, philosophy, the cognitive sciences and anyone with an interest in better understanding this central concept within the complexity and systems theory framework.