This unique textbook ? made up of classroom slides and relevant context from the authors? course at NYU ? provides a clear, step-by-step journey from the fundamentals of signal analysis to the sophisticated modulation and detection strategies that power today?s communication systems. Beginning with intuitive treatments of Fourier Series, Fourier Transforms, and Nyquist?s Sampling Theorem, the book builds the mathematical intuition students need to move confidently into analog and digital modulation techniques?covering AM (DSB, SSB, VSB), FM, PM, and their behavior in noisy environments. The narrative then turns to modern digital topics such as sampling, quantization, coding, and probabilistic detection for binary and multi-signaling schemes, showing how error probabilities can be driven arbitrarily low with thoughtful waveform design. Rich in worked examples and practical insights, the text equips undergraduates with both the theoretical grounding and hands on perspective required to understand, analyze, and design real world communication links. The book is designed for a semester undergraduate course in Fundamentals of Communication Theory, and the slides are intended to be used and are available digitally.