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In this book, some types of pseudo BH-algebra and pseudo ideals of pseudo BH-algebra (pseudo P-ideal, pseudo q-ideal, pseudo a-ideal, pseudo multiplicative ideal, pseudo positive implicative ideal, pseudo completely closed ideal are given. This book consists of three chapters, chapter one deals with some basic concepts of BCK-algebra, BCI-algebra, BCH-algebra, BH-algebra, (subalgebra, associative, normal, regular, implicative, positive implicative, essence and ideal of BH-algebra) with some propositions, theorems and examples. Chapter two is devoted to study some types of pseudo BH-algebra, pseudo ideal, pseudo closed ideal, pseudo completely closed ideal, pseudo P-ideal, pseudo q-ideal, pseudo a-ideal, pseudo implicative ideal, pseudo positive implicative ideal, pseudo sub- implicative ideal pseudo BH-algebra and pseudo essence BH-algebra, some theorems, propositions and examples are given to describe the properties of these notions among, in chapter three the relationships among pseudo ideals. Also, the notion of pseudo BH-homomorphism is introduced.