The kernel is the core component of an operating system that acts as a bridge between hardware and software. It manages system resources, including the CPU, memory, I/O devices, and file systems, ensuring that applications have controlled and secure access to these resources. As the primary part of the OS, the kernel operates in a privileged mode (known as kernel mode) to execute critical tasks and enforce system security.

A kernel is the central and most privileged component of an operating system that functions as an intermediary between the hardware and application software. Formally, it can be defined as a set KKK of functions and services:K=(R,M,P,S)K = (R, M, P, S)K=(R,M,P,S)

where:

• RRR represents resource management, including CPU, memory, and I/O device allocation.
• MMM denotes memory management, which includes virtual memory and physical memory handling.
• PPP refers to process scheduling and management, involving task creation, execution, and termination.
• SSS stands for system call handling, providing controlled access to hardware resources and kernel services.

Operating in privileged kernel mode, the kernel ensures system security, process isolation, and efficient multitasking. Depending on its architecture, the kernel can be monolithic, microkernel-based, or hybrid, each with trade-offs in terms of performance, security, and maintainability. It plays a fundamental role in maintaining the stability, efficiency, and security of the operating system.

Kernels are broadly categorized into types such as monolithic kernels, microkernels, hybrid kernels, and exokernels. In monolithic kernels, all essential operating system services (e.g., device drivers, memory management, and scheduling) run in kernel mode as a single entity, ensuring high performance. Conversely, microkernels maintain only minimal functionalities in the kernel, moving most services to user space, which improves modularity and system reliability but may lead to performance overhead. Hybrid kernels blend the advantages of both architectures.

Key functions of the kernel include process scheduling, memory management, interrupt handling, and system call management. It ensures multitasking by allocating CPU time efficiently and uses virtual memory techniques for optimized memory utilization. By managing system calls, the kernel provides an interface for user applications to request hardware operations safely and efficiently. The kernel’s stability and efficiency play a crucial role in the performance and security of an operating system.