There isn't much available in English which is hardly surprising given that this was a war with next to no English participation. (Much like you won't find a wealth of books about the ECW in Polish or Swedish.) And of course there is the ever present language barrier.
Robert Frost's has published two books about the period
After the deluge : Poland-Lithuania and the Second Northern War, 1655-1660 (1993)
and
The Northern wars : war, state and society in northeastern Europe, 1558-1721 (2000)
Neither is particularly good due to Frost strong pro-Polish bias which at times has him resorting to using methods such as cherry picking, quote mining and even the wholesale invention of events to give the Poles a boost and bash western military methods in general and those dastardly Swedes in particular.
A couple of samples from the Northern Wars
"…the highly effective Swedish cavalry tactics after 1621 were based on Polish examples, although it was not until the eighteenth century that most western armies replaced their straight cavalry swords -little more than pointed clubs – with the curved Polish sabres which were far more effective as cavalry weapons."
Let's see, Swedish cavalry tactics were not based on those of the Poles, 'western' armies retained straight cavalry swords as late as WW1 and not only were 'western' swords not "pointed clubs" but highly effective weapons which were arguably more versatile due to being well suited to both cut and trust.
Some "pointed clubs"
linklinklinkA fairly basic study of the subject would have avoided these errors.
Frost describes the Swedish breakout from the Vistula-San encirlement in 1656 as follows:
"Forcing his way over the San under cover of darkness on 5-6 April he broke through the Lithuanians, who had no infantry or guns. It cost him most of his artillery and much of his baggage, together with a relief force of some 4500 cavalry and dragoons which had set off from Warsaw under Margrave Frederick of Baden (…)"
Oddly this supposed loss of Swedish artillery and baggage has not been recorded by either Polish nor Swedish sources, indeed Jan Wimmer whose work on the war Frost's lists in his bibliography describes first how the Lithuanians delayed the Swedish building of a bridge using firepower (i.e infantry and artillery) and later how the Swedes moved off with their artillery on barges after the Lithuanians had retreated. No mention is made of the supposed Swedish losses.
In fact it was the Lithuanians, not the Swedes, who lost artillery and baggage when the camp was overrun by the Swedes after the assault across the San.
Likewise the Swedish force led by Margrave Frederick have been given a 50% increase despite Frost having access to Wimmer who quotes an accurate strenght of 2500-3000 based on Swedish primary sources.
If you can find a cheap copy of the Northern Wars it is worth picking up a flawed introduction to the wars but it is not worth paying full price for IMO.
While not focused directly on the war with the Commonwealth you can find bits and pieces of interesting information in
Brian Davies
Warfare, State and Society on the Black Sea Steppe, 1500-1700 (2007)
and Carol Steven's
Russia's Wars of Emergence 1460-1730 (2007)
There is nothing in print in English about the Swedish army during the 2nd Northern war AFAIK. I do have a post about the uniforms worn in 1655 on my blog at link
I will be posting more about the Swedish army during the Deluge now that By Fire and Sword has been translated English and my own interest in the period has returned.
rusmilhist.blogspot.se has lots of information about the Russian army in particular but also bits & pieces about other participants in the war such as the Swedes & Imperials.
