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This is a well-written introductory textbook for meta-analysis. Several major topics for meta-analysis (such as Fixed effect model, Random effect model, Subgroup analysis, Meta-regression, Publication bias) are introduced. These topics are followed by simple numerical examples, called "workout examples". Since the workout examples are very detailed, the readers can easily track the calculations.
   One of the most important and interesting topic is the demonstration of the difference between the fixed effect model and random effect model. The book uses many diagrams (particularly forest plots) to explain the conceptual difference. Quntitative difference between the fixed and random effect model are also explained well (via the difference of the  weights assigned to each study).
   This book does use mathematical formulae, but it does not use very complicated ones. Whenever the mathematical formulae appear, the authors try to explain their meaning. I very much enjoyed reading the authors' clear interpretation of the formulae. But, the derivations of the formulae are mostly omitted, so this is not the book of Math.
   Note that this textbook is only restricted within introductory level. I suppose that real meta-analyses may not be as simple as the book describes. For instance, this book rarely discusses "individual patient data (IPD)" which may be necessary to perform truely reliable meta-analysis. Another topic that this book does not cover is the survival data analysis.  However, this drawback is supplemented; the references to journal papers, softwares, Websites, and books are extremely useful for furthere study.
  As the title "Introduction to" claims, this book should be a perfect starting point before learning more advanced and specific meta-analysis. Especially, readers can understand the goals and fundamental tools for meta-analysis without going through some technical aspects. After reading the whole textbook, I am convinced that meta-analysis is a promissing scientific tool in many fields. In my view, this book will be cited in academic journals in biostatistics, such as Biometrics, Stat. Method. in Med. Res., and Stat. Med.

Suitable level; Master or Ph.D. in Statistics / Master or Ph.D. in other fields such as Medicine, Biology, and Phycology.

This book includes modern theories for asymptotic analysis (or large sample analysis), which will be useful for mathematical statisticians. Empirical process techniques are used as a main tool to prove theorems. I found that functional delta method (Sec. 20), Z-/M-estimators (Sec. 5), U-statistics (Sec. 12), influence function (Sec. 20) are very helpful for studying asymptotic behavior of statistics commonly used in non- and semi-parametric inference, especially in survival analysis. The book also feature many classical topics such as Bahadure efficiency, LeCam's lemmas, etc. Overall, many theorems are difficult to prove. This may be because the theorems are given for minimal (weak) regularity conditions, which leads to technically long proofs. I found the section on semiparametric models (Sec. 25) not read well due to the highly abstract (and  partly unclear) explanations. 

Suitable level: at least Master in Statistics or Mathematics. More suitable for Ph.D. or Professors in Statistics.

The study of copulas in statistics has a long history but is still vigorously growing. This book covers the fundamental mathematical properties of copulas useful for students, statisticians, and probability theorists. As I know, this book is the most standard books for copulas The book is quite easy (and comfortable) to read from its clear explanations and elegant proofs. Also, the proofs are mostly follow from simple results of analysis which is tought in undergraduate mathematics (without measure theory or functional analysis).
   The book starts with the definition of copulas and the Sklar's theorem in Chapter 2, and then gives the definition of Archimedean copulas in Chapter 4. In Chapter 4, there is a list of 22 Archimedean copulas, which is an extremely useful reference for people who work on copulas. Chapter 5 studies the dependence structure of copulas, such as Kendall's tau and Spearman's rho, which are again an extremely useful reference.

This book describes the theory of empirical processes and thier weak convergence. The book comprises empirical process theories (Chapter 1 and 2) and statistical applications (Chapter 3). As a statistician, the most usuful is Chapter 2, in which M-estimator, Z-estimator, Fuctional delta method, etc. are described. Especially, Section 3.3  (Z-estimator) present a very general theory of Z-estimators, by which I find useful in studying the nonparametric maximum likelihood estimator (NPMLE).

The theorems and their proofs are usually difficult to understand. The main difficulty comes from the generality of the treatment. For example, Z-estimators treated in this book takes its value in Banach space (usual Z-estimators take their valus in Euclidian space in semiparametric or parametric models). Hence, readers need some abstract thinking to understand the mathematical objects. Nevertheless, this generality of the treatment makes the theory of Z-estimator very powerful and applicable, especially for studying the NPMLE.

From theoretical point of view, the book carefully treat the mesurability problems. It is surprising that empirical procecess are not Borel mesurable function (p.3). To relax the measureability issues for empirical procecess, the book adopt the Hoffmann-Jorgensen type arguments to drop the masureability requirements. This is interesting. 

Suitable level: at least Master in Statistics or Mathematics.  More suitable for Ph.D. or Professors in Statistics. Very difficult and challenging book.

This book summarizes wide range of topics in mathematical statistics. No real data analysis is included. I had a chance to read this book to teach a required course for Ph.D students. The major reason that I like this book is the right coverage of materials. They includes important classical results that are supposed to be learn for students who major in Statistics.

Chapter 1 is compact but very dense introduction to propability thoery, including the measure theoretic definitions of Radon-Nikodym derivative and conditional expectation. This measure-theoretic treatments of the probability have at leaset two purposes: 1) unify the discrete and continuous distributions into a single framework ; 2) define advanced probability concepts (conditional expectation, martingales and Markov chain). If the readers are familier with probability theory, it seems okay to skip Chapter 1 and start from Chapter 2 (Fundamentals of Statistics).

Chapter 2 provides a decision theoretic framework that include point estimation, interval estimation, testing, etc. It also includes fundamental concepts that are useful to evaluate the performance of estimators, including admissibility, minimaxity, consistency, etc. This chapter also covers shrinkage estimators in simultaneous estimation. This section seems to be the most important and interesting part of the book.

Chapter 5 study hypothesis testing. I found this section the most difficult to read since theories of UMP, UMPU, UMPI are quite abstract and the proofs are less clear. This difficult may partly due to the less organized arrangements of the theorems: there are too many equation numbers in theorems and lemmas; there are too many statement in theorems. For examle, Lemma 6.7 contains so many equation numbers that I almost felt annoying to follow.

Sometimes, the description of the book become so general and abstract that I felt difficulty in teaching. For example, the descritpions for the LSE and BLUE focus too much on the identifiability conditions of the parameters, without little real example. In addition, some derivations of the formulas are not clearly written which makes it difficulty to follow. For example,

A number of excercises listed at the end of each chapter is useful for teaching and homework assignment (but students can easily find answers from the internet).   

Suitable level: at Master or Ph.D students in Statistics or mathematics.  It is not easy for students without math background.

The book nicely explains multivariate analysis based on very clear, step-by-step presentation, using lots of matrix algebras. Many data examples are also used to illustrate the formulas and theories in this book. The author emphasize the geometrical interpretation of the results. Geometrical interpretation is well-explained in general, but it is sometimes not too easy to understand if the reader is not familier with linear algebla. Although the title of the book includes "Applied", the contents of this book seems to be more interesting for "theoretical" or "mathematical" statisticians, especially they like to interpret the result geometrically.  Since the description of the linear algebra is so nice,  the book can be a useful reference for linear algebra.

Suitable level: People who finish linear algebra.

One of the standard textbooks for survival analysis.  This book characterizes survival analysis as techniques for handling "incomplete" data such as right-censored data. This style is rather different from standard textbooks in which survival analysis is introduced as a technique for handling right-censored lifetime data only. In fact, most textbooks on survival analysis do not treat left-truncation, which is one of the important areas in survival analysis. Therefore, the book becomes a particularly useful reference for thoese who are interested in analysing left-censored data, left-truncated data, right-truncated data, inteval censored data and competing risks data. The methods are explained with lots of real data examples from medical research.

Suitable level: People who finish linear algebra, calculus and elementally probability theory.

One of the benchmark text book for reliability and survival analysis . I do not read all chapters of this book, but the Chap 2 (Failure Time Models) and Chap.3 (Inference in Parametric Models) are useful for studying reliability (I publish one paper in Technometrics by studying this book). Especially, the book gives consice description of "industrial life testing" using the motorettes examples, a well-known example in the industrial life-testing context. The so-called Weibull regression implemented in "survreg" routine in R follows the formulation of this book. Overall, the book is useful "reference book" for writing academic papers, as it includes modern topics in a wide range (e.g., Chap10, Analysis of Correlated Failure Time Data).

In addition, Chap. 8 (Competing risks and multistate models) includes the authentic overview of cause-specific and cumulative incidence analysis for competing risks data. The well-know identifiability issue for competing risks data is also given. The description is good enough. However, there are better books, e.g. Classical Competing Risks by M. Crowder (2001), to study competing risks.

In general, there are many equations whose derivations are unclear. Hence, students may requare energy and time to understand the book without  instructors.

Suitable level: Master or Ph.D students in Statistics.