This is a weird book. In some respects, it's a wonderful resource. In other respects... it's not really clear who the intended audience is, or why. Unfortunately, it's made a little superfluous by the existence of the internet.
I bought this book as a teenager, when I was just starting to be interested in linguistics; I was frankly disappointed. Despite the title, there's very little of substance here about the languages of the world.
The book has three parts. Part I is an assignment of around 600 languages to their families and subfamilies, followed by brief descriptions of the major families. Like all attempts at linguistic family trees, there are many dubious points here; in particular, it must be said that the first edition of this text is from 1977. Some editing had been done by the time of this third edition - the USSR has become 'the former USSR' - but other archaisms remain. Katzner still speaks of Chari-Nile and Saharan, for example, rather than Nilo-Saharan (and not because he has a modern suspicion of Nilo-Saharan, but rather because he hasn't heard of it yet). Khoisan is still treated as one family, rather than three (or five, given that he includes Hadza and Sandawe as a 'branch') unrelated families with areal influences - and he still uses words like 'Hottentot' (though he does put 'Nama' in brackets, and he does note that he's using the traditional and prevalent names for the sake of continuity). In general, these problems aren't that serious, due to later editing or because Katzner is generally a splitter - there's no Uralo-Altaic or Hokan here (there is 'Papuan' and 'Paleo-Asiatic' (our Palaeo-Siberian), but they're noted explicitly as geographical terms of convenience). Although there is Altaic, which I guess there wouldn't be today. Anyone looking for a family tree of languages must be prepared to realise that many of these issues are still highly contested, and probably always will be.
[similarly to 'Hottentot', there are a few other potentially aggrevating word choices - he talks of 'Indian' languages, for example, rather than 'Native American'; however, these should be understood as an attempt to use the established language terms of the day for the purposes of clarity, and not as indicating any particular prejudice of thought.]
The family description are sparse; only Indo-European gets an actual comparative wordlist, and only IE and Afro-Asiatic get a breakdown into subfamilies. The information in each description is mostly accurate (although he says that Old Church Slavonic was first written in Cyrillic! (no, it was in Glagolitic)) and sometimes interesting, but is in effect a casual presentation of disorganised trivia - we learn that the capital of Abkhazia is Sukhumi; that most speakers of Mundari live to the north of the speakers of Ho; that Grebo and Bassa are members of the Kru branch; that Ge'ez ceased to be spoken in the 11th century (though it continues in use for liturgical reasons); that there are (were?) 750,000 speakers of Berber in Mali; that Khoisan has clicks; that the word 'petunia' is of Tupian origin; that Hiri Motu (the creole that the Motuans developed with their sundry trading partners) used to be known in English as Police Motu; and so forth. Some of this information is out of date factually (like speaker numbers, I'm sure!) or theoretically (he postulates an extremely slow population of the Americas by people of diverse physical appearance; in fact the genetics now seems to show an astonishing rapid settlement by people who were at first very closely related to one another). There is almost no information about the languages themselves, as languages - the subentry on Afro-Semitic, for example, does not even mention non-concatenative morphology.
In general, this collocation of random facts, with a particular fascination with mentioning capitals of countries and regions, and listing the particular scripts used for each language, strongly suggests that the author was a mildly interested amateur enthusiast, rather than a linguist. Indeed, although the author did also compile a Russian-English dictionary, apparently his main literary endeavour was in assisting the compilation of encyclopaedias, and that... kind of fits.
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The second part of the book is basically a linguistic sampler: a page (sometimes two) on each of 200 notable languages. Each language gets a small text sample, a translation, and anything from one paragraph to a whole page or so of trivia facts. Sometimes this is about the history of the speakers, or the script, or the regions where it's spoken, or it dialects, or any other random thing. We learn, for example, that two thirds of Ossetian speakers live in North Ossetia (capital: Vladikavkaz), that Ossetian is believed to have been separated from other extent Iranian languages by about 2,000 years and that it has been strongly influenced by the neighbouring Caucasian languages, that there are two main dialects (Iron is more widely spoken than Digor), and that Ossetian can easily be recognised by its use of a letter that looks like an o-e ligature, not otherwise used in Cyrillic. We learn that between 1927 and 1940, Turkmen was written in the Latin script (to which it transitioned back after 1991). More than half of the speakers of Madurese actually live on Java; the Buginese alphabet is believed to be derived from the Kavi script. Etc.
Again, this information is unsystematic, superficial, and frankly I wouldn't want to rely on it anyway.
And yet there is some value here. It does serve to introduce a range of important languages to a casual Western audience - if it doesn't really tell us much about these languages, it does give us some superficial familiarity with them, and that's not a bad thing. How many people in the West have even heard of, say, Nyanja, let alone knowing that it's more correctly known as Chinyanja, and that it's the principal language of Malawi, spoken by (including the populations in Mozambique and Zambia) 7.5 million people? I mean sure, it's actually spoken by at least 12 million people (as of 13 years ago), and when he confusingly says that in Malawi it's known as Chewa, he means that its official name since 1968 has been Chichewa, but it's still known as Chinyanja in Zambia. But even the inaccurate information is more than most people have.
The book also helps give a feel for the sound of these languages, through its samples. Nyanja (Chichewa) sounds like this: Anzace Sanalikumuwelengela Koma iye Sanadzipatule. Whereas here's some Papago: Sh am hebai ha'i o'odhamag g kakaichu. Kutsh e a'ahe matsh wo u'io g ha'ichu e-hugi. [and yes, if you're suspicious it is indeed a form of O'odham].
Unfortunately, whatever superficial impression we can get from this is of course absent for all the languages not in the Latin script, unless we also happen to be able to read Greek, Cyrillic, Buginese, and so forth. While these other scripts are interesting in their own right, it would have been nice to see all the languages in romanisations. And it must also be said that there is no phonetic information here, let alone grammatical analysis - this is as superficial as possible.
It's also blatently wrong. Katzner obviously doesn't speak most of these languages, and I'm pretty sure, just comparing proper names, numbers of sentences and so forth, a bunch of these 'translations' aren't actually of the given text (I think that's true of the Chichewa text, for example). And while some of these texts are interesting poems, or fragments of stories, from which cultural information may be tantalisingly glimpsed (I love the opening of the (alleged) Chichewa text, for instance: Once upon a time there lived a man whom his community generally regarded as an idiot. In spite of this he did not isolate himself. (happy ending: the idiot throws a small stone into the eye of an elephant, killing it, after it was weakened by the real hunters. Well, happy ending for the idiot, at least)), others are... not. The Bemba text appears to be a dry encyclopaedia entry about how many languages there are in Africa.
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The short third part is a survey by country, listing the official and several of the most spoken languages for that country, often with some geographical information and speaker numbers. This is potentially useful, although of course it's liable to be out of date.
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So. As a scholarly resource, this book is, to put it gently, useless. The information may be out of date, and in any case cannot be relied upon for accuracy. The information of languages and language families can all now be found easily on Wikipedia or other such resource, in more detail than here, and with more reliability; likewise, the most 'useful' part of the book, the country survey, may be conveniently concise, but only duplicates information found easily online. And above all, there is no information here beyond the most superficial and trivial.
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But on the other hand! No, this is not scholarly; it is not a useful resource to be relied upon. But it probably wasn't meant to be. The blurbs use words like 'delightful' and 'buffet', and 'non-specialist': the intent here is not really to inform, but to inspire.
So let's imagine I got this book 5 or 10 years earlier. Would I still have been disappointed? No, I'd have adored it!
What a book like this can do is open a person's eyes to the wonderful, delightful diversity of human language, and to the sheer largeness of the world. It can have a similar effect on certain children, I would imagine, as an encyclopaedia can - sure, the information may be superficial, and unreliable, but it's not meant to be the last word. It's the first word. It shows people where the words can be, and leaves them to go find more of them themselves. And I think it could have the same effect for certain adults. But there it's more difficult, because it properly belongs to a very specific moment: the moment where you realise you want to learn about the topic, but haven't really started yet. At THAT moment a book like this has a value, reassuring you, yes, there's so much to learn here.
Unfortunately, that is a narrow line - too much knowledge, and this book is disappointingly superficial and annoyingly wrong. Too little knowledge, and this book could be overwhelming in its barrage of facts. So how big its ideal readership is, I really don't know. But I do still think that that readership is out there, somewhere. Perhaps.
[N.B. Goodreads says this was first published in 1975; the text itself, however, says it was first published in 1977; my copy is a third edition from 2002]
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P.S. it's so charmingly out-of-date in some respects that its three examples of artificial languages are Esperanto, Interlingua, and... Occidental! Ah, that's so cute (and out of date even in 1977 - Occidental was forced to rename itself as Interlingue in 1949, for reasons of censorship). Sadly we don't get an Occidental text, though.