The basic book is an attractive hardcover rulebook with extensive notes on setting, culture, religion and politics in Dark Ages Scandia. Of course, there's the core rules system for character generation, combat and magic and an introductory scenario as well as atmospheric interior art (B&W and colour) and a (rather primitive) map.
The setting is an interesting one. This is NOT the Viking Age, but the Age of Migrations that preceded it, the age of Beowulf, Hengist & Horsa and King Arthur (who, along with the British setting, is explored in the companion game Keltia). As such, lifestyles are a bit more primitive than the fully pomp of the Viking Era: the kingdoms of Denmark, Sweden and Norway are only just forming, much of the land is unexplored and the stuff of legends blends with historical dynasties in an entertaining way.
By the way, back at university I ran a well-received fantasy campaign in exactly this setting. It never got named, except as "Brownie Quest", and used rune stones instead of dice. It was very pretentious but, for a bunch of college kids, very engaging. It's great to go back to that world again with Yggdrasil.
This is definitely a FANTASY game. Sweden is ruled by "sorcerer kings" and Norway by "half giants". The gods make personal appearances, along with trolls and krakens. Yet at the same time, it's a political game where the three kingdoms (plus the `wild card' Gautar) jostle for pre-eminence through marriage, assassination and war. The introductory scenario nicely sets this tone, sending the PCs on a quest to visit a sorceress to decipher a dream but involving them in a calamitous love affair that affects the destiny of nations.
Some of the fantasy features might not be to everyone's liking. For instance, women are according full warrior status and smiths seem to specialise in making dinky, figure-enhancing chainmail for them to wear. Historically, quite silly, but it's (a) a concession to female gamers and (b) a literalist porting in of certain figures from myth and legend into the historical setting. Gamers may retain or drop this aspect of the world, according to taste.
Although not a Viking RPG, some of the Age of Viking features have been retrospectively introduced, such as the makeup of the classical Aesir (Odin as Allfather, Thor and Frey, etc). In this period, this religion is slightly anachronistic, but it is familiar.
I'll be GMing Yggdrasil with Odin as necromancer/trickster and Tyr as Allfather, but this is a minor gripe.
In other ways, the Norse setting is carefully honoured. The `dwarfs' and `elfs' (dwergar, alfar) are not the dwarves and elves of Tolkien but the rather more elemental demi-deities of the North. Another excellent supplement,Nine Worlds, explores the supernatural setting in more detail.
The game mechanics are fairly simple, a bit blunt and clunky but certainly not committing the cardinal sin of over-complicating barbaric combat. You roll d10s and keep the best two to add together. Rolls of 10 'explode' enabling you to build up super high scores. Valuable buffs let you keep 3 dice; unpleasant weaknesses only let you keep one. The system has a fluid "roll with it" feel. You choose general Strengths and Weaknesses and draw Fate Runes representing areas of life in which you can expect to do better or worse. These all have the same effects: letting you keep extra dice or fewer dice when working out your total.
There's a tripartite magic system which is, again, slightly clunky, focusing on Seidr and Galdr `spell lists' and a rather more freeform rune magic that I suspect more experienced roleplayers will prefer. The Seidr spells are classical mage stuff - cursing and healing and controlling the elements. Galdr spells are sung and are the specialism of skalds (bards); they include charms and illusions. Rune magic gives buffs to people, objects or places.
The roster of characters is somewhat limited by the setting. Basically, you can be a warrior, possibly a noble or a berserker, or else a sorcerer, either a tholr (shamanic priest), volva (enchantress) or skald (poet/illusionist). Instead of classes there are broad templates, so you can create a warrior jarl who knows a bit of rune magic, but you will be substantially underpowered compared to characters who specialise. The rules hint at more exotic characters from other ethnic backgrounds - like the Gautar and the Finns among human tribes or mystical creatures like half-giants - which may be developed in future supplements.
One of the problems with games like this is the limited cast of characters. The writers want to be true to the (fantastical) period, so really you're going to be a warrior or a witchy-wizard or a berserker. Starting with the more outré characters only makes it harder to get into the historical setting, but sticking to the stereotypes might be frustrating for experienced gamers. I'm going to push for people to use the pre-generated character templates at first. Once people are happy with the world, they can bring in the half-trolls and Saxons.
What makes characters in Yggdrasil interesting is the way their fate is mapped out by three runes. In a fairly flexible way, the runes provide bonuses and penalties when the themes they embody arise in the story. I routinely use runes or tarot in roleplaying to simulate fate so this is a welcome feature for me and I encourage other gamers to explore this. The runes used in this game are (appropriately enough) the 24 runes of the Elder Futhark - tough to pronounce but close enough historically and conveniently grouped into three thematic sets of eight. You can buy a set of rune stones cheaply and they make a great accessory to them game - I'm not recommending actual fortune telling because, you know, it's a fantasy RPG, but they add atmosphere.
Overall, a functional RPG system with some imaginative flourishes in an intriguing setting. The scenario is of a high standard and the supplements, develop an intriguing campaign. I suspect the greatest strength of Yggdrasil will emerge when it can be combine with Keltia, offering a very different way of exploring the Arthurian legends from the `classic' approach taken by King Arthur Pendragon.