Read James Campbell's Introduction to remote sensing first and Lillesand, Kiefer and Chipman's Remote sensing and image interpretation second. Campbell is the gentler of the two standard course texts, strong on image interpretation and on why the discipline developed as it did, and it assumes essentially no mathematics beyond secondary school. Lillesand is the more comprehensive — photogrammetry, thermal, radar, lidar and digital analysis all covered properly, with the physics introduced as needed — and it is the one that stays on the desk.
Be clear about what the rest of the path assumes, because this is where people underestimate the subject. From stage two onward: multivariable calculus, linear algebra including eigen-decomposition, undergraduate probability and statistics, and enough physics to be comfortable with electromagnetic waves, blackbody radiation and Fourier transforms. From stage four, some scripting in Python, R or MATLAB. Both of the introductory records are early printings of long-running texts — Campbell is now co-authored with Randolph Wynne, and later Lillesand editions are substantially updated on modern sensors — so buy the most recent edition you can find.
The physics that makes the numbers mean something
W. G. Rees's Physical Principles of Remote Sensing is the best single treatment of the underlying physics at a level a competent undergraduate can follow: electromagnetic theory, radiometry, atmospheric interaction and the physics of each sensor type, with the mathematics worked rather than asserted. It needs calculus and comfort with wave physics. Elachi and van Zyl's Introduction to the physics and techniques of remote sensing is the harder and more complete treatment, the standard graduate text out of JPL, covering wave propagation, interaction mechanisms, orbital mechanics and every sensor family including radar interferometry; it assumes electromagnetics at physics or electrical-engineering degree level.
The point of this stage is to be able to derive rather than recite the sensing chain — source radiance, atmospheric transmission and scattering, surface interaction, sensor response, digital number — which is what makes radiometric and geometric correction something other than preprocessing you skip.
Digital image processing and classification
John Jensen's Introductory Digital Image Processing is the standard applied text on Earth-observation imagery specifically, explaining preprocessing, enhancement, classification and accuracy assessment with the practitioner's questions in mind; it needs statistics and comfort with matrices. John Richards's Remote Sensing Digital Image Analysis is the rigorous treatment of the same material — Bayesian classification derived properly, feature reduction, spectral transforms — and requires linear algebra and probability at a real level. It is the book that turns you from someone who runs a classifier into someone who can say why it failed. Schowengerdt's Remote sensing, models, and methods for image processing, catalogued with commas in place of its colon, gives the signal-processing view and is the strongest of the three on image formation: point spread functions, resampling, the frequency domain, image fusion. It assumes Fourier analysis and explains artefacts the other two teach you to work around.
The specialist sensor families
Radar defeats people who skip the fundamentals, because the intuitions carried over from optical imaging are actively misleading. Iain Woodhouse's Introduction to microwave remote sensing is the most humane introduction in print and genuinely is an introduction, building the wave physics carefully before scattering and imaging radar. Massonnet and Souyris's Imaging with Synthetic Aperture Radar is the step up — synthetic aperture formation, speckle, polarimetry and interferometry, from two authors central to the development of InSAR for ground deformation — and it assumes signal processing and complex analysis. Read it before touching Sentinel-1 phase data. Manolakis, Lockwood and Cooley's Hyperspectral Imaging Remote Sensing treats a hyperspectral cube as a statistical signal-detection problem, which is the correct frame and rarely taught this well; it is heavy on linear algebra and detection theory and the most demanding book on the path.
Doing it on real data
Morton Canty's Image analysis, classification, and change detection in remote sensing closes the gap between algorithm and code: each method derived, then implemented, with the MAD and IR-MAD change-detection material better than anywhere else. Later editions use Python and Google Earth Engine. Cloud-Based Remote Sensing with Google Earth Engine is the modern workflow in the platform where most applied work is now actually done — the full Landsat and Sentinel archives already on the server, analysed in place instead of downloaded — and it is tutorial-led and open access. Wegmann, Leutner and Dech's Remote Sensing and GIS for Ecologists is a worked applied pipeline in R for people with a domain question rather than an imaging one.
Finally, Paul Bolstad's GIS fundamentals is the one to read in parallel rather than last if your GIS is weak, because the errors that ruin projects are usually projection, datum and topology errors rather than classification ones. The full ordered path is at /paths/pt_ai_remote-sensing-and-satellite-imagery.