This lecture covers fundamental notions in digital filtering, including 2D filtering approaches, linear filters, transfer functions, frequency responses, stability issues, FIR and IIR filters, and filtering by convolution or differential equations. It also discusses zero phase FIR filters, frequency domain filtering, image processing, and Gaussian filters. The instructor explains the concepts with examples of filtering, up-sampling, polynomial filters, Laplacian approximation, and sharpening techniques.