This book contains a number of papers by leading researchers discussing their work on either geoacoustic inversion (GI), signal processing (SP), or reverberation. It is intended for scientists entering these fields as well as for experienced researchers. Chapter 1 (Tolstoy) begins the section on GI. It is a review article covering the main topics of GI and mentions such subjects as matched field processing (MFP), improved source localization and tracking, array element localization, propagation and parameter modeling, search methods, the nature of the search spaces, improving efficiency, sensitivities and uncertainty, benchmarking, and applications to simulated and test data. It is intended as a resource for understanding the GI area as well as for locating key references. Chapter 2 (Dosso) describes one of the most successful and most applied methods for GI: a Bayesian approach using a hybrid simulated annealing (SA) variant for optimization and Gibbs sampling to characterize the posterior probability density. The formulation is discussed here in mathematical detail. The emphasis in this chapter is on rigorous uncertainty estimation where the unknowns are considered to be random variables constrained by the data and prior information. Errors are assumed to be Gaussian distributed for the derivation of some key equations, and statistical tests are presented to support this assumption. Data from the PROSIM 97 experiment at numerous frequencies are analyzed. Chapter 3 (Chapman & Jiang) discusses the interpretation of matched field inversion results, particularly their limitations, and illustrates their analysis using multifrequency experimental data from the New Jersey continental shelf site that was selected on the basis of high spatial and temporal coherence across the array. They are concerned with the impact of data errors due to parameter correlations in Bayesian inversions, and the effect of the bottom slope in three dimensions (they conclude that only two dimensions are needed for their inversions). Chapter 4 (Michalopoulou & Nolte) begins as a review of Bayesian source localization methods but is primarily concerned with one such approach which the authors developed: the Optimum Uncertain Field Processor (OUFP). This is an approach used for target localization and tracking which reduces sensitivity to environmental mismatch by incorporating prior information. The method also produces posterior distributions permitting the quantification of uncertainty and error estimation of calculated parameters including environmental properties. Moving and multiple sources are discussed. Chapter 5 (Taroudakis) discusses modal inversion techniques in shallow water. Modal observables such as modal phase, modal arrivals, and dispersion curves using both the time and frequency domains are incorporated into linear and non-linear inversion procedures. The methods are based on geophysical analysis using normal mode propagation. Good separation of modes is required which is affected by the nature of the array and the frequencies used for the inversions in a given scenario. Chapter 6 (Baxley) is a review of the use of GI primarily to: (1) show results of simplified approaches to GI, (2) review the SWellEX experiments of 1993-1999 as a good testbed of GI, and (3) perform inversion using horizontal as well as vertical line arrays. The intention was the optimization of system performance for the localization and tracking of undersea targets using a variety of arrays and the Bartlett processor. Range-independence was assumed so that a simple normal mode model could be used. A number of parameters were estimated using a number of frequencies (less than 200Hz) assuming a simplified bottom. Chapter 7 (Rajan et al.) is a complete and mathematical discussion of modal inverse techniques. The chapter presents a formulation of the inverse problem, an estimation of the modal eigenvalue, demonstrations in RI and RD waveguides with discussions of error sources, spectral estimation, modal attenuation coefficients, sediment characteristics determined from modal dispersion data, integral equations, matrix inversion, resolution and variation of estimates, further demonstrations of inversion success for simulated and test data, and more. A complete coverage of modal issues is presented here. Chapter 8 (Tolstoy) is the final chapter on GI and concerns a volumetric (tomographic) GI method. This approach combines individual 2-D (range and depth slice) inversions on multiple arrays and for distributed sources into a full consistent 3-D (range, depth, and azimuth) image of the region bottom. It is discussed within the context of the Haro Strait test and concludes that information about array geometry (phone depths and shape) is essential for successful inversion where success is defined as high MFP values (at any and all frequencies with good signal-to-noise) at a unique set of parameters. Additionally, 3-D resolution may be improved via regularization to counter scarcity of resources. Chapter 9 (Arvelo) starts the section on signal processing with a detailed discussion of the factors affecting system performance, particularly at low frequencies (below 1 kHz). These include noise, especially as it affects coherence (temporal and spatial), waveguide variability (such as bathymetry), and scattering processes. A review of low-frequency coherence modeling and measurements is presented, and examples are provided to illustrate key points. Methods to circumvent the hard limits imposed by spatial coherence include the exploitation of multiple dimensions, such as the design of planar and volumetric arrays. Seismic coherence is also discussed. Chapter 10 (Sullivan & Candy) is a review of passive synthetic aperture processing (PASA). This approach to array processing utilizes the (towed) array motion to enhance its performance by explicitly incorporating this motion into the signal model. Historically, its name is based on the idea that the improved performance is equivalent to effectively having a longer array (the array appears to be larger when multiple phone locations can be combined coherently, and this approach is most effective for short aperture arrays). It is unique in that it treats the problem as a recursive estimation process rather than a beamforming process. Again, the primary interest here is system performance. Since it recursive in time, its application is limited to continuous signals (such as radiated noise) as opposed to short-term signals (such as pulses). The authors present the PASA development in mathematical detail (narrowband and broadband, single and multiple sources) including both simulated and experimental data. Chapter 11 (Zurk) completes the section on signal processing where concerns about waveguide mismatch are addressed by the development of more robust processing methods. Rather than attempting to determine ocean properties, many signal processors concentrate on the goal of devising techniques less dependent on the channel nature with the intent of improving system performance in uncertain environments. This can involve incorporating the statistics of the environment, using a calibration source, or developing invariant (robust) processors. These approaches are discussed here. Chapter 12 (Gauss) is the only chapter to concentrate on reverberation and presents a review of active sonar components coupled with signal processing for the purpose of detecting, localizing, and tracking undersea targets. Incomplete knowledge of the environment and clutter (reverberation from non-targets) are the primary limits on system performance. Clutter mechanisms include: bathymetry, the ocean surface roughness, fish, bubbles, and more. These mechanisms and methods to control their influence using frequencies 50 Hz to 5 kHz (single frequency and broadband), in deep and shallow water scenarios, are discussed. Deconvolution is critical to all reverberation efforts. Additionally, Doppler effects can be also used to separate signal contributions. The chapter concludes with a summary of contemporary issues and future trends. Finally, the observant reader will notice that this text is dedicated to Leon Sibul. Leon died quite unexpectedly early in 2007 with the intention of contributing a chapter to this book. We in the research community miss his mathematical insights and contributions to signal processing. We miss the chapter he would have given to us in this book. But most of all, we miss him.