There’s 8 parties there - the 9th block in grey is ‘övrig’ - others
Ok, this is tricky but, from left to right
V - Vänsterpartiet
Left party, split from the Social Democrats in the 20s. Called themselves communists up until 1990. Main current policies; renationalisation of schools, hospitals, elderly care, transport etc. Anti militarism, pro-feminist. For higher tax on business and lower income tax. Increased dramatically due to voters returning from the feminist party who dared not waste their vote on the party falling under the 4% and therefore outside govt
S - Social Democrats
Traditional Socialist party in Sweden and Sweden’s biggest party historically. Could compare them to Labour - they come from a similar trade union background. Currently with Stefan Löfven in charge they are pretty close to what a Corbyn Labour might look like but they have been further to the left previously (Olof Palme for example)
Mp - Miljöpartiet
Green party. Politically fairly central in Swedish terms but with obvious left leanings socially and prioritise environmental issues with a combo of regulation & investment in green technologies. Pretty similar to UK Greens
C - Centerpartiet
Centre party. Ronseal. Historical background support from rural communities but modernised effectively in recent years partly due to their very visible and vocal leader Annie Lööf who, despite being only 35, has been party leader for 7 years. Not really analogous to any UK party
L - Liberalarna
Liberals. Very much like the Lib Dems in many ways. Formerly called Folkpartiet - people’s party. Traditional party support among teachers and education questions are their specialty
M - Moderaterna
Moderates. Tories pretty much. Classic right wing neo-liberals these days, were earlier much more socially liberal. Friends of big business of course
KD - Krist Demokraterna
Christian Democrats. Formed in the 60s to maintain influence of the Swedish Church when church & state officially separated but no official ties to Swedish church. Their main platform issues are elderly care & childcare but they are veraciously small government, lower taxes, deregulation etc.
They have picked up hugely in this election campaign mainly thanks to the fawning cult around their party leader Ebba Busch Thor;

Who, among other things, is a total islamophobe
SD - Sverige Demokraterna
Sweden Democrats. Anti-immigration, nationalists, racists. Openly said that muslims aren’t Swedes, that Jews aren’t Swedes - privately that they aren’t even human. UKIP but with political nouse & votes & cash & a LOT of supporters in certain regions
Hope that helps